First of all, I’m going to go out on a limb here and assume (this may not be true but again I’m assuming, so sue me) that you haven’t read the comics. Never fear, that’s why I’m explaining this to all of you :)
Tony and Steve are the ‘mom and dad’ of the Avengers and it’s a theme that’s commonly poked at.
There are many panels in the comics that poke fun at the fact that Tony and Steve act like a married couple, bickering over remotes and having arguments that cause the ‘children’ to worry.
See it’s like a running gag. Anyways, on to how Peter fits into all of this. There are many moments in the comics where Peter treats Steve and Tony like a son would treat their parents. And he has called them mommy and daddy before.
And yeah that’s basically it. Peter is sort of the ‘son’ of Tony and Steve because he treats them like parents. And the entire Avengers group treat Tony and Steve as the mom and dad of the Avengers.
So yeah that’s where the whole superfamily thing really comes from. The fact that Steve and Tony are basically married and everyone knows it and accepts it except for Steve and Tony.
For some extra superfamily joy, look how happy the Avengers look when mommy and daddy make up after a REALLY bad fight: