jigsaw family
n. A household that includes two or more sets of children from the parents' previous relationships.
William Higham, founder of consumer trends company Next Big Thing, said the rise of ‘jigsaw families’ meant that escaping for a break is no longer just about mum, dad and two children.
Linking-up the finances of complex, interlinked jigsaw families is difficult work — and more often than not the CSA struggled.
—Tom Clark, “Welfare reform bill live blog: government suffers sixth defeat,” The Guardian, January 25, 2012
2002 (earliest)
Madonna and Guy Ritchie are increasingly representative of modern British families, according to Virgin One.

Virgin said the traditional married couple with 1.6 children was increasingly being replaced by "amalgamated" or "jigsaw" families where one or more of the couple have children from a previous relationship.
—“Virgin guide aimed at untraditional families,” Financial Advisor, May 29, 2002