Here's what you're likely thinking of:
* The "wall-to-wall television" families: The people in Fahrenheit 451 often substitute real family relationships with the constant stream of entertainment provided by their "wall-to-wall television" sets. These screens are often referred to as "the family" and provide a constant barrage of images and sounds, keeping people from engaging with the world and each other on a deeper level.
* The "substitute family" of book-lovers: Throughout the novel, there is a sense of community and shared experience among those who read books, even though they are officially outlawed. These book-lovers find a sense of belonging and understanding with each other, forming a kind of "family" built on intellectual and emotional connection.
While Bradbury doesn't use the term "parlor families," he clearly demonstrates the way technology, in this case television, can both isolate and connect individuals in a society. The characters who choose to break away from the "parlor families" and embrace real connection, whether through books or genuine human interaction, are the ones who are able to find true meaning and fulfillment.