Dib and Gaz's relationship is very tumultuous, as Gaz hates her brother with every fiber of her being, and will go out of her way to punish him if he crosses her. Dib is older than Gaz by a few months or possibly a year, but sometimes it seems like Gaz is older in terms of maturity. On very limited occasions, Gaz does show some kindness to her brother, but they never last long.
The constant abuse that Gaz gives to her brother has caused controversy from Christians and the now defunct magazine called Christian Parenting Today.
In "Dib's Wonderful Life of Doom", when their father, Professor Membrane, says that his DNA seems different than what is normal, Gaz says "I guess I'm sorry about being so mean to you all those times" with a grunt. However, since this was part of an illusion created by Zim, it's unlikely that she would have actually said this. If Dib is in horrible peril and she is forced to help him, she will. But it is seen that Dib isn't always the nicest to Gaz, either.
In "NanoZIM", Gaz helps him navigate the micro-suit throughout his body, albeit thinking the whole thing is an online video game and not actually Dib operating a microsuit in an effort to save his brain.
In "Gaz, Taster of Pork", aside from them holding hands (although the series creator has stated it was an animation error), Dib casts a spell on Gaz, but feels bad after he finds out the effects. He tries to reverse it to the best of his ability. Meanwhile, though he likely recognizes this on some level, Dib is somewhat obligated to watch over her and rarely seems to be intentionally trying to annoy her.
Despite their constant clashes, they will occasionally work together, and there is the rare moment where they seem to get along like family. Dib, however, does sometimes seem to be irritated with Gaz's negativity, such as in "Bloaty's Pizza Hog" when he responds with a "Uh huh, whatever" when Gaz makes fun of his obsession with saving Earth.
In "Dark Harvest", it's shown that Dib cares about Gaz and wants to take care of her when he sees her in the cafeteria and it looks like she's in pain (even though she was merely playing her Game Slave, which was placed into her body courtesy of a certain alien). And in "Gaz, Taster of Pork", after coming clean about his original intentions and fearing his sister has failed her test (which in fact she passed), he begs the hog beast to spare her and punish him instead. Even though it turns out there's really no need for either of them to suffer, Dib is punished and recieves no mercy for his sacrifice - especially from Gaz.
In "Dib's Wonderful Life of Doom", Gaz and Dib are seen quarrelling just like any other pair of siblings would. After hearing from her father about Dib having super powers, she says in a monotone voice, "I guess I'm sorry for being so mean to all those times". However, this was only a dreamlike illusion created by Zim in the hopes of finding out if Dib was the one responsible for throwing a muffin at him during lunchtime earlier.
As seen in "The Wettening", Gaz seems to be purposefully mistreating her brother, reeling herself in after accidentally letting slip an interest in what he's doing.
However, their relationship is mostly strained. Whenever Gaz is playing on her Game Slave, she doesn't like to be bothered, as demonstrated in the episode "Dark Harvest". In "Future Dib", Gaz is sent by their father, Professor Membrane, to retrieve her brother. When Zim's Dib Robot-Spy doesn't obey her, she beats it up, which unintentionally saves the day. In "Backseat Drivers From Beyond the Stars", Gaz states that "Dib's voice... fills me with a terrible rage!". Their father does little to break up their fighting, especially since he is usually gone.
Gaz isn't exactly on Zim or Dib's side when it comes to Zim's plot for world conquest, as she thinks they are both foolish. In "Gaz, Taster of Pork", she tells the Shadowhog that Zim is too "dumb" to take over the world, and that she shouldn't have to listen to Dib's constant ranting about him.
Although they fight often, they do live in the same house, and try to act civil on some occasions. They also seem to be pretty much that each other has; seeing that Dib does not have any friends, and Gaz is usually seen alone (it's unknown if she has friends). They seem to always sit together at the same table at lunchtime.
Despite her annoyance with Dib's obsessive nature and her generally mean behavior toward him, her actions in "Mopiness of Doom" show that she is unhappy when he stops pestering her about the paranormal, going so far as entering his room with a drawing she made about that night's Mysterious Mysteries episode to entice him into coming downstairs, stating that Dib should be "annoying" her right now.
While she might simply be irritated by the sudden change altering her routine, she also sees that Dib isn't truly happy when he isn't pursuing his real interests, and perhaps even feels lonely or ignored without her brother rambling on at her. Although Gaz is mean to her brother and enjoys torturing him and causing him pain, she would also defend him if someone else caused him to go beyond an acceptable level of Dib suffering. 
In Invader Zim: Enter the Florpus, Gaz is disgusted with how out of shape Dib's become from his obsessive waiting for Zim's return, and later makes fun of him wearing his trench coat again. Later on, she shows annoyance when she suspects he's going to hijack their father's keynote speech to expose Zim; when Zim himself then takes over the speech after abducting and replacing Membrane, imprisoning Dib and Gaz in their own house in the process, Gaz angrily blames Dib for it, and apparently tries to escape several times without him. Despite this, when the two are later caught and imprisoned while trying to rescue their father from Moo-Ping 10, Gaz doesn't heap any further blame on him, despite him expecting her to. As she explains, she only treats him as badly as she does because she knows he can take it, and seeing him as despondent as he is at this point is too much even for her, showing that she does care for her brother.
Jhonen has stated that one of the things he wants to do with the comic series is expand on Dib and Gaz's relationship, presenting them more as siblings. In the first issue, Gaz is shown annoyed and disgusted by how out of shape Dib's become, and by his singing of his own workout montage music while trying to get back in shape; Gaz provides the music instead, just to help get him back to being less disgusting.
In Issue 3, Gaz mocks Dib's obsession with Bigfeet by revealing she's already met him and taken pictures with him that are now posted online. After making fun of Dib's reaction, Gaz mentions that Zim is on TV posing as an artist. When Dib decides to investigate Zim's newest plan, Gaz pretends to be excited about joining him, but then reveals she's just messing with him.
In Issue 5, Dib shuts off Gaz's online game to force her to spy on Zim with him. In retaliation, Gaz recruits their father's help to find an alternate universe where gamers rule and non-gamers are enslaved as NPCs. After taking over this world, Gaz kidnaps Dib and makes him an NPC, making him suffer horrible pain through countless games until he apologizes for interrupting her games for his own interests. She then releases him and they go home, where they play a video game together with Membrane; but when Dib wins, Gaz calls him a cheater and throws him through a wall.
Gaz only appears in two scenes in Issue 9. In the first, she uses Membrane's Flesh Printer to give Dib a convincing disguise to pass himself off as an alien intern, in order to infiltrate Zim's base; when he asks if it'll hurt, she says that it doesn't have to, but makes it so that it does anyway. In the final scene of the issue, she tells Dib to shut up his anguished screaming (over no one liking his video), as it's distracting her from her game.
Gaz again only briefly appears in Issue 10, where she accompanies Dib when he goes to spy on Zim's base. However, she makes it clear that she's only tagging along because he bribed her, and when he jumps on the Voot Runner as it's taking flight, she shows no interest, merely walking away and saying that she's going to have their father put Dib's dinner in the refrigerator.
Gaz makes another brief appearance in Issue 11, when Zim tries attacking Dib with a robotic cat. When it fails to trigger an allergic reaction (as it lacks dander) and Zim complains about Dib not becoming hideous, Gaz comments that Dib is already hideous.
In Issue 14, Dib is going to explode if he becomes too sad due to unknowingly ingesting nanoexploder bots. Gaz feels guilty since she was the one responsible for giving him the vial of nanobots to drink. She goes to great lengths to make sure he doesn't become sad, even participating in his paranormal investigations even though it's obvious that she does not enjoy it. She does this not only to save his life, but also because it's his turn to pick the restaurant for family dinner night and she wants him to pick Bloaty's Pizza Hog. During that dinner, when the nanobots wear off and his life is no longer in danger, Gaz tosses Dib's pizza in his face.
In Issue 16, Gaz is willing to help Zim terrify Dib in exchange for access to alien games on Arcadikon. However, her efforts are rather halfhearted, possibly indicating that while she doesn't care enough about Dib to not aid Zim, she's also not totally willing to help harm him.
In one of Dib's stories in Issue 17, when Gaz sees that Dib has brought pizza for all the Skoolchildren, she proudly announces to everyone that he is her brother and calls him "the best". However, it is possible that Dib made up or exaggerated this story, given that this is also the case with all the other stories told in the issue.
In Issue 21, an accident with one of Zim's machines causes Dib and Gaz to switch bodies with GIR and Zim, respectfully. Initially, Gaz doesn't care much about the situation, but then Dib tries to convince her to use it to try and defeat Zim for good. Gaz seems to agree to this, convincing Zim to accept a bet that she can do a better job of taking over Earth than him, telling Dib that it's a ploy to destroy Zim's operation from within. Within days, Gaz has set herself up as a benevolent alien philanthropist, with Dib concerned at how much power she's gathering. Finally, at the issue's climax, Gaz reveals that she intends to outright steal Zim's identity and rule the world, leaving Dib devastated at his sister tricking him. In the final scene, it's shown that Gaz banished Dib to the moon alongside Zim (who was banished for losing the bet).
In Issue 32, Gaz states that the only way that she can stand to talk to Dib is by using an AR helmet to make it look like his head is an entire monkey. She also tells him that he should give up on his fight with Zim, as it's getting embarrassing.
In Issue 33, Gaz makes it clear that she doesn't care about Dib's attempt to beat Zim in the Innovation Fair, and when he mentions that inventing runs in their family, she angrily asks that he stop reminding her that they're related. Later, when Dib is setting out on a quest to find out what Zim's plan for Mr. Wiener Face is and swears to not come home until he does, Gaz tells him that he doesn't need to come home at all.
In Issue 38, when GIR is impersonating Dib, Gaz is the only person to see through his disguise. Seemingly surprising herself, she decides to do the real Dib a favor, telling GIR that in order to properly impersonate Dib he has to try and prove Zim is an alien, thereby indirectly ruining Zim's plan.
In Issue 44, during the Membrane family's trip to Meat Mountain, Gaz is annoyed by Dib's focus on whatever Zim might be planning, telling him that it's getting embarrassing and that he should just focus on their vacation; she also has no problem mocking him for his poor skiing skills. At the end of the issue, she gets angry at Dib for how his saving of all the other skiers from Zim's plan means that they're now stuck behind them on line for the resort.
In Issue 50, Gaz gets angry at Dib for eating some mini donuts she was saving. To get back at him, she encourages Chammy Wamboo in her efforts to make Zim and Dib become friends, knowing that Dib will be annoyed by it. Dib seems to be aware of this, as when Chammy notes that Gaz let her into their house to talk to him and calls her sweet, Dib sarcastically agrees.
In Quarterly 2, Gaz blames Dib for the situation when Membrane's reputation is damaged by him not believing that GIR is the Beeboogoat and demands that he fix the situation. She then travels cross-country to join her family, interrupting Dib's attempt to expose Zim as an alien and forcing him to stay focused on helping their father.
In The Dookie Loop Horror, Gaz throws Dib through a wall for eating the last of the honey ghosts cereal. When he has a feeling of deja vu (caused by the time loop he's trapped in), she comments that it's because she throws him through walls all the time, then casually admits that she saws his head open at night and stuffs things inside it for fun.
Facts of Doom
- Their relationship is similar to the relationship between Ed and Sara on Ed, Edd n Eddy, in that they're a kind older brother and a more violent younger sister.
- Some fans think their father, Professor Membrane, is the reason why they rarely ever get along because he is rarely ever home with his kids and he is supposed to be responsible for them.
- Dib Membrane
- Gaz Membrane
- Dib and Tak's Relationship
- Ms. Bitters and Dib's Relationship
- Dib and Zim's Relationship
- Gaz and Zim's Relationship
- Gaz and GIR'S Relationship
- Dib and GIR's Relationship
- Dib and Professor Membrane's Relationship
- Gaz and Professor Membrane's Relationship
- Dib and Zita's Relationship