Whereas marriage is still the dominant framework to raise a family, competitive partnerships emerge. Facing the increasing proportion of couples likely to cohabit rather than marry, some provincial governments of Canada have enhanced the commitment related to cohabitation to protect women and children in case of separation. To understand the effects of such a policy on couple formation, assortative matching and within-household allocation of resources, we need an equilibrium model of marriage. In this paper, I propose a search and matching model of marriage with two types of contracts where men and women draw utility from private consumption and leisure, and may invest in a match specific good. The model is estimated on Canadian data. I then use this model to show how enhancing commitment of cohabiting couples might change the entry and exit rate into cohabitation and marriage, impact assortative matching and the within-household allocation of the total resources.