Are the Simpsons a nuclear family?

Answer 1

Since the term "Nuclear family" is used to define a family group consisting of one or more children living with two parents who are married to one another mostly and are each biological or adoptive parents to all children in the family...

Yes, they are.

Answer 2

Since the series began in 1969 to me they seem to predate nuclear families. I think of them more as a product of the Cold War.