Yes, isn't it actually the 'living together' thing?
Though this isn't often stated in as many words, it's just the throwing together of different characters into the business of living alongside one another and seeing what comes out.
For those of you with long enough memories, most of Tony Hancock and Eric Sykes's stuff was built around this. In the modern era, I'd make a case for The Young Ones, Only Fools, Men Behaving Badly and Father Ted as being obvious examples.
Even things like Red Dwarf could be said to be of the genre.
After all, isn't it CHARACTER humour which is the essential? Any actual reliance on the 'situation' to keep producing the humour is a blind alley IMHO.
Feel free to add any others of the ilk. Anyone remember The Liver Birds??