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We explore whether stable matchings and trade in commodities can coexist. For this purpose, we consider competitive markets for multiple commodities with endogenous formation of one- or two-person households. Within each two-person household, individuals obtain utility from his/her own private consumption, from discrete actions such as job choice, from the partner’s observable characteristics such as appearance and hobbies, from some of the partner’s consumption vectors, and from the partner’s action choices. We investigate competitive market outcomes with an endogenous household structure in which no individual and no man/woman pair can deviate profitably. We find a set of sufficient conditions under which a stable matching equilibrium exists. We further establish the first welfare theorem for this economy. Copyright Springer-Verlag Berlin Heidelberg 2015