There are many sociological constructs for a family. Therefore, it is impossible to group all units together under one definition.
Low-income families function differently to high-income families. A “traditional” family with one parent of each gender has different characteristics to single-sex families, adoptive families, foster families, and estranged families. Families without children but with older dependents function differently to families with young children, which function differently to families with older children. It is not possible to pin down one single sociological definition for the diversity of “family” units. 
A cross-cultural approach with a wide enough sample can, and has, defined the family unit. Families across the world share certain traits. They live under a shared roof. They have some level of economic dependency and integration, and the reproduce in some capacity (either biologically or through adoption/fostering). These criteria are applicable to family units across the world, whatever guise or form they take.
[P1] There are too many variables and forms to accurately define the notion of a family under one sociological definition.
Rejecting the premises
[P1] With a wide enough sample, a pattern emerges which allows for the deduction of a sociological definition of a family.