Professor Membrane is the father of Dib and Gaz, but he has very little time for his offspring, being one of the most famous and important people on Earth.
The Professor, as he is often called, is rarely at home, so he supervises his kids in the form of a floating monitor, which often spews out pre-recorded reminders that are often way out-of-date. Expectedly, Dib and Gaz refer to him as Dad.
Although his parenting skills seem to be missing in action, he really does love his kids, taking time at least once a year for dinner together—and always remembering to activate the food monitor. In "Future Dib", he invented a device that would supply unlimited energy to the entire planet, but refused to activate it unless his children were there to share the moment.
Membrane is somewhat embarrassed of his son's belief in the paranormal, refusing to call it a "proper" branch of science. However, he believes Dib's obsession is just a phase (or as he speaks of it, "temporary insanity"), that Dib will eventually grow out of, and allows his son to do as he pleases to an extent. He even understands that letting go of such of notions isn't easy, comparing it to how he once believed sharks and humans could be friends (which cost him both his arms). On occasion, Membrane is so preoccupied with work that he fails to recognize his own kids (i.e. not recognizing Dib when he comes backstage in "Battle-Dib").
Professor Membrane has also had a grudge against Santa Claus ever since he was a child; on Christmas day, instead of giving him twelve cases of Uranium-238 as he'd asked, Santa gave him a present overflowing with socks.
In the comic series, the Professor is presented as a more active parent, spending more time with his children. This is carried over into Invader Zim: Enter the Florpus, where it's made clear that despite still not liking Dib's obsession with the paranormal, he's proud of and loves his son.
Appearance
Professor Membrane's appearance has not developed much since he was a child, other than his increased height. He wears a white lab coat, purple gloves, and big black boots. His eyes are never clearly seen due to him wearing goggles. Dib looks a lot like his father, both sharing black hair styled in similar scythe-like shapes.
For Invader Zim: Enter the Florpus, the Professor has been slightly redesigned, with more hair on the top of his head in addition to the scythe, as well as a thicker coat that makes him look thicker than he did in the series. Also his gloves and boots are now larger, the gloves acting to cover the fact he now has cybernetic arms (with it being heavliy implied that they were lost in a vicious shark attack when he was a child).
In "The Most Horrible X-mas Ever", Membrane seems to have incredible power, similar to that of Dib's power in the episode "Dib's Wonderful Life of Doom", when he blasts open the back door with an energy beam fired from his glove, although this is likely based more upon technology that he created rather than any natural gift. This was eventually confirmed in Enter the Florpus, wherein it is revealed that the Professor has two completely robotic arms hidden under his gloves, which are capable of firing powerful energy attacks. He apparently lost his real arms to sharks he tried to befriend as a child.
Role in Invader Zim
Membrane is based on many real-life scientists and inventors, such as Nikola Tesla and Stephen Hawking. He has a science TV show Probing the Membrane of Science, which is similar to Bill Nye the Science Guy, which requires the people in the audience to pass several tests just to sit and watch. He is somewhat of a celebrity, and was described in "Future Dib" as someone "without whom the whole world falls into chaos".
The Professor appears to be about 40 or so; his first name is unknown, but none is apparently needed; he is world-renowned for his contributions to human science, making breakthroughs in every scientific field, from genetics and neuroscience to disease research and engineering. Some of his most notable inventions include the hover helmet, the Perpetual Energy Generator (which was never put into use, due to heckling from the crowd) and Super Toast.
Had the series continued, it would have been revealed that Dib and maybe Gaz as well were not actually Membrane's birth children, but had been genetically engineered by the Professor, perhaps as an experiment. This may explain why Dib and Gaz seem to have superhuman powers, as well as the lack of a mother in the Membrane household. However, this idea was never brought to fruition.
In the comic series, Membrane is presented as more of an active parent, as he's seen spending more time having meals with and playing games with his children, in person rather than by remote. However, he's also demonstrated that he still prioritizes science over them - in Issue 5, he agrees to help Gaz imprison Dib in an alternate universe ruled by gamers just because she says it's for science; in Issue 16, he's happy to let Dib use an experimental fear siphon, even though he admits it's not ready for human use yet; and in Issue 32, he shows only moderate concern for the fact that Dib intends to cheat at the Physical Fitness test, instead being more focused on something he's needed for on the Moon.
In Invader Zim: Enter the Florpus, Membrane has his largest role ever. Intending to use his new Membracelets to harness the power of children holding hands around the planet in order to improve the world on Peace Day, he is dismissive of Dib's return to studying the paranormal. This causes an angry Dib to decide to crash his father's keynote speech unveiling the Membracelets in order to expose Zim, who has become despondent upon learning the Irken Armada isn't coming to conquer Earth. However, learning of the Membracelets inspires Zim, and he hijacks the speech, taking over Membrane Labs and sending Membrane himself to Moo-Ping 10, before using the Membracelets to teleport Earth into the Armada's path, inadvertently creating a dangerous Florpus Hole in the process.
Dib and Gaz eventually use Tak's Ship to reach Moo-Ping 10 and rescue their father, who is convinced the whole thing is a hallucination caused by being hit on the head. Despite this, he is able to deduce how Minimoose can be used to reverse Earth's teleportation before the Florpus destroys it. Tak's Ship then breaks the Membranes out and they fly back to Earth, only to crash due to debris. Membrane is separated from Dib in the crash, but tracks him down in time to save him from Zim's robot soldiers. Despite still believing that the whole situation is a dream, Membrane fights the robots, destroying all of them, only to be confronted by Clembrane, a flawed clone of him created by Zim; confused by the clone's presence, he is defeated by it. Fortunately, when Gaz's intervention causes Clembrane to get ahold of Minimoose from Zim, she and Dib are able to convince him to hand the moose over.
Membrane then uses Minimoose to return Earth to its proper place, just in time to avoid it being destroyed by either the Florpus or the Armada. Afterwards, he has dinner with his family (now joined by Clembrane), and reveals that he still believes that the whole thing was a hallucination.
In TruthShrieker, it is revealed that his last name is Membrane.
The Professor was the final member of his family to have met Zim and by extension possible the first scientist to have met an alien, though he is unaware of this fact as he thinks Zim to be a child with a skin condition.
Professor Membrane knows Zim as Dib's "little foreign friend" which makes sense as he (somewhat erroneously) believes that he is from another country rather than another planet (this could refer to the fact that "alien" is also a synonym for "immigrant").
He also said in one episode that if there truly were aliens in space then they would be too far away and believes that not one of them could travel the massive distance to our planet, completely unaware that Zim is an alien from space and that he survived the massive trip to Earth.
Jhonen Vasquez revealed that Professor Membrane is rich which makes sense seeing as he has his own TV Show "Probing the Membrane of Science", creates several inventions that he most likely patented, has two labs, one downtown and the other in the basement in his house and it is hinted in "Future Dib" that he also gets funding from the government as he is friends with President Man.
Despite possibly being the smartest man on Earth, the Professor still can't tell that Zim is an alien Invader, unlike his children who can.
Professor Membrane seems to have a deep and strong loathing for the fact that Dib actually successfully re-awakened the living dead and won't let Dib forget it, even though Dib said he was sorry.
He doesn't allow Dib to use his tools for his "para-science", as stated in the Halloween episode. However, this is contradicted in "NanoZIM", when he allows Dib to use his nanoship, although it's possible that the Professor made these restrictions after an unseen event in the series, maybe the above mention of bringing the dead back from the grave.
The Professor has a lever built into his home for restoring power to the entire city, in the (apparently frequent) event that his son causes a city-wide blackout.
He has on a couple of times in the series called Dib "my poor insane son."
In "Battle-Dib", it's revealed in his autobiography that the professor's first sentient thought was "I will poop now".
In "Future Dib", there was going to be a future version of himself who is presented as a head in a jar in a floating robotic body, as seen from the concept art by Aaron Alexovich. This was probably inspired by Futurama, which had a similar concept in which the heads of famous people are kept alive in the 31th century by being preserved in jars.
Since the Nanoship's controls he created that were seen in "NanoZIM" strongly resembles the Game Slave, it may hint that Professor Membrane is a bit of a gamer himself. Another clue was in "Game Slave 2", when he said that "video games develop hand eye coordination, and make kids into better human beings!", and later in Issue 1 of the comics he was seen playing a video game with Gaz.
The Professor calls Gaz his "funny child" and sometimes he even calls her "honey". He sometimes even calls her by her name which he never does to Dib, implying that she is his favorite child and may be protective of her.
The feeling must be mutual since unsurprisingly, the Professor is Gaz's favorite family member.
He knows that Dib's voice angers Gaz greatly, but still has her go up into his room to spend time with him and hopes that her company will help Dib become "less insane."
Jhonen Vasquez has said in the commentary for "Future Dib" that he had trouble with one of Professor Membrane's colleagues calling Dib and Gaz his "roommates" rather than his kids as he feels that joke while it does highlight him as an absent figure in their lives he does love his children.
In the unmade episode "Mopiness of Doom", Professor Membrane could actually tell Dib was unhappy following his turn towards "real" science, since a formula he got from him was incorrect and the Professor believed it was a "cry for help", and for once gave him some fatherly advice. Of course, this just ends up backfiring as he unintentionally encouraged his son to be a paranormal investigator once more.
Despite the Professor not recognizing Dib and often being embarrassed by his "para-science" he does love his son as Jhonen Vasquez has said that without his father, Dib would've been dead long ago, one example of this could be seen in "Bad, Bad Rubber Piggy" when he made the MegaBoy 3000 to save his son's life.
The Professor has a little handmade puppet version of himself and seems to have a talent for ventriloquism. However, this may just be because his mouth is covered by his clothing.
He's the creator of Super Toast and of the Perpetual Energy Generator (also known as P.E.G.).
In "The Most Horrible X-Mas Ever", during a flashback when the Professor was a kid, he sounds as if he's already an adult.
In the series Professor Membrane is scrawny with a single scythe looking hair. However, in Invader Zim: Enter the Florpus, he seems to have a full set of hair and gained some weight.
In the movie it's also revealed that Professor Membrane has robotic arms, his real ones having apparently been lost to sharks he tried to befriend as a child.
The scene in Enter the Florpus where Professor Membrane yells "Not scientifically possible!" at a random crowd member quickly became a meme.
Melissa Fahn played Professor Membrane during InvaderCON 1, as Roger wasn't invited as a guest at the time.
Professor Membrane's name is based off of a membrane, a thin film-like structure that separates two fluids.
Professor Membrane may well be a very vain individual, considering how highly he talks of himself and his studies. Not only that, but he has a lamp of himself in his own home.
Jhonen Vasquez chose to make Professor Membrane a scientist so Dib could have access to advanced technology he could use against Zim's advanced Irken Technology.
Professor Membrane has made it clear that he'll do anything if it's stated to be "for science", no matter how morally questionable. It's how he justifies imprisoning Gaz and turning her into a media freak during "Gaz, Taster of Pork", and in Issue 5, Gaz weakly using it as her reasoning for finding a dimension ruled by gamers and imprisoning Dib in it is enough to get Membrane to go along with it.
In Issue 16, he allows Dib to use an experimental Fear Siphon, despite admitting it's not safe for human use yet. Combined with the above mentions of doing anything "for science", this implies the Professor has a very loose set of morals.
This issue also shows that, despite being a man of science, he seems to be unaware that humans have already landed on the moon, as he states that the Fear Siphon's slurry could one day be used as fuel to reach the moon. However, in Issue 32, he claimed to be needed there and made it with nothing more than his lab coat and a space helmet, which could imply that the Fear Siphon was involved in his ability to travel, but is most likely merely another case of the series' loose continuity ignoring a previously established fact for the sake of a gag.
In Issue 44, it's revealed that the Professor has an RV with his hairstyle on top of it.
In the same issue, it's shown that he thinks that Minimoose is one of "nature's deformities", which would explain why no one questions why he's purple or can float.
It's revealed in the same issue that the Professor is surprisingly skilled at skiing.
This issue marks the first time that Professor Membrane doesn't wear his lab coat and instead wears winter clothing.
Gallery
Membrane as a child on Christmas, seconds before he opens his life-changing present of socks.
Membrane with puppet self
Professor Membrane having dinner with his kids in the series
Membrane having dinner with his kids in the comics
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