There are three basic uses for "family home" that I can think of.
First, a "family home" is a term used in real estate to describe place to live that is designed for a family, as opposed to an apartment or condominium/duplex.
Another reason someone might use "family home" is if they are wealthy and own other homes that they either rent out or vacation in. The "family home" would be the primary residence. And another home might be called a "rental property"/"rental home" or a "summer home"/"winter home."
The third use would be the home belonging to the parents of grown children. When everyone comes together for a holiday, for example, they might say, "We're going to the family home."
However, "family home" is not a phrase that is used very often in conversation. All of these uses are fine, but more often people will say the same idea in a different way.