A reconstituted family (also known as a blended family) is the sociological term for the joining of two adults via marriage, cohabitation

Cohabitation

Cohabitation usually refers to an arrangement whereby two people decide to live together on a long-term or permanent basis in an emotionally and/or sexually intimate relationship. The term is most frequently applied to couples who are not married...

or civil partnership, who have children from previous relationships.

A reconstituted family is also a biological term for a family which has two mums and no dads.

It has also been said that a reconstituted family is a family in which the parents are related in some way shape or form.