A theoretical framework that describes the equilibrium of species in a multicomponent membrane is presented. This framework considers explicitly first-order nonidealities that describe the interactions between pairs of species in a multicomponent membrane (e. g., Nafion). These binary interaction parameters are fit to methanol and water uptake data for liquid methanol solutions. A chemical model is combined with this framework to describe uptake of water vapor by the membrane over the entire range of relative humidity. The framework established here provides a means to describe the gradients in electrochemical potential for species in the membrane when describing the driving forces for multicomponent transport in a second companion paper. This paper describes equilibrium conditions; the second paper considers nonequilibrium conditions (transport and reaction kinetics). The modeling aspects are combined in a third paper to simulate the direct methanol fuel cell and quantify aspects of its design.