First of all I'll have to break the characters in two groups, because you cannot compare old people with children. So the first group will be composed of Lisa and Bart (the children) and the second one of Marge and Homer (the parents).
Just by taking a glance at the show you see that it portrays the typical image of the "traditional American family" of the last decade: mom stays home to cook, clean and take care of the kids, while the husband provides for the family. The little boy is very violent doing a lot of "cool" things, and of course never studies, while the little girl is very quiet and smart.
There are certain traces of stereotypes in almost all the activities in which the characters engage and that seems to be meant in a funny way. For example, in one episode, Lisa and Bart are taken hostages by a prison escapist in a zeppelin. Using a computer inside the zeppelin you could write on an electronic board outside the zeppelin. Lisa discovers that and writes a message to let everybody know that they are in there and in the middle of it she puts these flashing red hearts... I wonder if they would have done that if Bart were the one writing the message!
This other time Bart gets himself a fake ID, rents a car and goes away for spring break with some friends (he of course lies to his parents); meanwhile Lisa stays home and has fun by going to work with her dad. What's the message here? Boys go off and do crazy things, but girls must stay home, close to the family.'
Bart is always the one who has all the adventures and does all the exciting funny things and Lisa is the smart quiet one always getting him out of trouble. She never holds any grudges, while Bart is mean to...