Most of the following information comes from Brotherhood and / or the Manga, however some information is purely my own speculation or on the encounters Envy’s had during my roleplays, and is not officially stated anywhere else. (I will use a * as indication for what is cannon and what is speculation.)
Envy’s older, favourite sibling. They get along extremely well- minus a few minor scrapes and usually work together to achieve their father’s goals. Envy is very fond of Lust and looks up to her in a way (although it might want you to think more otherwise) due to her being somewhat of a role-model for the genderless homunculus.
Like Lust, Envy is often tasked with baby-sitting Gluttony, or at least helping her baby sit Gluttony. Gluttony, being the most innocent and child-like of the homunculi sometimes annoys Envy with his certain dim-witted antics. Never the less, Envy would still prefer Gluttony’s company over that of most of its other siblings.
Envy and Greed don’t exactly get along and never have. In truth they fight like a cat and dog, constantly belittling and arguing with one another. Envy and the rest of the homunculi hold a certain malice towards Greed because they believe he betrayed them and their Father.
Envy doesn’t have a great deal of interaction with Sloth due to Sloth’s mammoth task underneath Central. *Overall it’s feelings for its lazy little brother are pretty neutral.*
Envy gets along with Wrath pretty well, sometimes they will squabble, but their augments rarely last long. Envy recognizes Wrath’s highly important role in his Father’s plans and holds some degree of respect for him as a fellow homunculus, despite him being a half-breed.
Like all the other homunculi (except for maybe Greed) Envy holds nothing but the utmost respect for It’s oldest sibling, Pride and follows his orders with little question. In truth, all the other homunculi fear Pride, knowing full well what their big brother is cable of. His authority over the other homunculi is second only to father himself.
Obviously Envy respects and cares for Father greatly, showing a huge deal of humility and gratitude toward Father for having given the envious sin life. Envy like it’s siblings- with the exception of Greed- work very hard to please their Father and help him in whatever way possible.
Solf J. Kimblee
Also known as the “Crimson Alchemist”, *Kimblee and Envy go way back to the Ishvalan war, where Envy first found Kimblee, and recruited him into the Homunculi’s despicable plan. Envy is as fond of Kimblee as a homunculus can be of a human, due to the man’s heretic ways.* They both get along quite well, as Kimblee enjoys the slaughter of his fellow man just about as much as Envy does.
Edward & Alphonse Elric
Envy sees the brothers as little more than a nuisance, however due to their important role in Father’s plans Envy is forced to tolerate the pair and even ‘look out’ for them in some instances to ensure nether of them are harmed until their usefulness to Father runs out.
Envy holds some malice towards Ling for near defeating the homunculus in an epic battle throughout Central’s busy streets (Manga version only). He is later forced to work with the Prince -after near killing him in another battle between himself, the price and Edward, inside Gluttony- when father decides to make the ambitious young Ling Yao his new Greed.
Envy holds particular malice towards LanFan due to her and her master Ling Yao near defeating it in a battle on the streets of central (Manga version only). Envy has little to no contact with Lanfan after this battle however.