cohabitation
noun /ˌkəʊˌhæbɪˈteɪʃn/
  /ˌkəʊˌhæbɪˈteɪʃn/
[uncountable] (formal)- the state of living with another person and having a sexual relationship with them without being married- There have been great changes in the patterns of marriage, divorce and cohabitation.
- cohabitation with somebody | cohabitation between A and B (figurative) a period of cohabitation between a conservative government and a socialist president