A household is a group of persons living together in a common housing unit or in a part of it, bearing together, at least partly, the costs of living (i.e. daily expenses, meals) on at least on of the days of the week they have a common lunch, dinner.
A household might consist of: one family, one family and their relative(s) living with, two or more families, two or more families and their relative(s) living with, one or more lone person.
Eventually there might belong to the household person(s) other than relative(s) (domestic help, person in state care, boarding student, person(s) supported for money, land or other property, etc.). Co-tenants, sub-tenants however always form a separate household.
Family
From the point of view of the census the family, the so called "family nucleus", is the smallest circle of persons living together as married couples or relatives of kin; they might be married couples without or with child(ren), lone parent (widowed, divorced, eventually never married) with never married child(ren). Male and female cohabiting (unmarried) partners together with their child(ren) should be regarded as a family as well.