A model of two-sided market (for credit cards) is introduced and discussed. In this model, agents can join none, one, or more than one platform (multihoming), depending on access prices and the choices made by agents on the opposite market side. Although emerging multihoming patterns are, clearly, one aspect of equilibrium in a two-sided market, this issue has not yet been thoroughly addressed in the literature. This paper provides a general theoretical framework, in which homing partitions are conceived as one aspect of market equilibrium, rather than being set ex-ante, through ad-hoc assumptions. The emergence of a specific equilibrium partition is a consequence of: (1) the structure of costs and benefits, (2) the degree and type of heterogeneity among agents, (3) the intensity of platform competition.