The answer is: stepfamily.
When idividuals end a relationship or a family unit, usally they look for another partners to form a new family. It would be considered a stepfamily, in the case of one of them or both have children. Since one of the them is the biological parent and the other is the stepfather, the latter can have legal ties with the child(ren). Both ties, blood and legal are present in this stepfamily.
