The definition of a family is often less than straightforward. Here is the definition of a family from the Census Bureau:
A family is a group of two people or more (one of whom is the householder) related by birth, marriage, or adoption and residing together; all such people (including related subfamily members) are considered as members of one family.
Naturally, now you need the definition of a householder:
The householder refers to the person (or one of the people) in whose name the housing unit is owned or rented (maintained) or, if there is no such person, any adult member, excluding roomers, boarders, or paid employees. If the house is owned or rented jointly by a married couple, the householder may be either the husband or the wife. The person designated as the householder is the “reference person” to whom the relationship of all other household members, if any, is recorded.