Introduced by Jack Stauber (artist and musiciant), a Cheeseburger Family represents the stereotypical "perfect" family : A couple of kids, one baby, a dad and a mom, all of that in a big house and with a lot of wealth. It may seems like a perfect family but is in reality very simple-minded.
The term "Cheeseburger" is used because it represents something almost everybody likes.
"Look at this Cheeseburger Family in this TV Movie"