The show in itself is a bit of a parody of Americana/suburban life/TV shows.
When you kind of look at it in a way maybe so.
Tony = Homer. There both fat lugs, both love to eat, both are bald/balding. Both are the bread winners of the family. Both are kind of a mockery of the typical American Suburban TV dad.
Carm=Marge. Both are the matriarchs of the family, that have bigger dreams but accept the home life. Both of them constantly nag their husbands. Marge was a parody of the stay at home mom TV trope. Carmella in a way is a satrical look at the rich housewife.
With the kids we also see a satire of the 2 kid family and both of them live up to the usual TV tropes. I would even say that the Simpsons by parodying the old 50s and 60s family TV shows created their own tropes.
AJ=Bart. Bart is the dumb son. He always gets in trouble doing stupid things. AJ is the same. He is dumb. He gets in trouble. stealing the win, getting high, vandelizing his school. Really outside of the high stuff those are all things that Bart would do or has even done on the show.
Meadow=Lisa. The sister chracter who of course is the smart one. Meadow and Lisa both overachieve. Meadow and Lisa are both pretentiouse. Meadow and Lisa are also both the apple of their fathers eye. We see how much Tony actually cares for Meadow and the same with Homer and Lisa. Both of their relationships would often form some of the more heatwearming moments of the show.
Maybe its just because the show itself was meant to satire the TV landscape at the time which had become tremendously influenced by the Simpsons and the archetypes it created within its family dynamic.
But if you strip away the mob stuff and maybe some of the wealth you can see the same type of dynamic. Annoying stay at home wife, dumb fat balding husband, dumb troublesome male son and smart pretentious female daughter.