The key factors that control the performance of perfluorinated sulfonic acid polymer electrolyte membranes cannot be deeply understood without a structural model of the material. Models of different complexity have been discussed in the literature. In this paper, we suggest a more detailed structural model of Nafion-type membranes, which results from a combined analysis of the ionomer molecular structure, data on swelling, small-angle diffraction, and conductivity as a function of water content. The analysis focuses on geometrical constraints on the self-organization of the polymer and possible patterns of phase segregation within it. The model identifies the percolation bottlenecks for proton transport and resolves controversies about the water-content dependence of the activation energy of proton mobility. It also suggests a new framework for molecular dynamics simulations of proton and water transport in such media.