open marriage
noun /ˌəʊpən ˈmærɪdʒ/
  /ˌəʊpən ˈmærɪdʒ/
- a marriage or relationship in which both partners agree that each may have sexual relationships with others
- Brian struggled to reconcile Anna's open marriage with his conservative views.
 - Her husband of 30 years proposed an open marriage, an idea that was devastating to her.