The permeability of certain polymer membranes with impenetrable nanoinclusions increases with the particle volume fraction ( Merkel et al. Science 2002, 296, 519-522). This intriguing discovery contradicts even qualitative expectations based on Maxwell's classical theory of conduction/diffusion in composites with homogeneous phases. This paper describes a theoretical model that captures the observed dependence of the bulk permeability and selectivity on the inclusion size and volume fraction, thereby providing a straightforward connection between membrane microstructure and performance. An essential feature of the theory is a polymer-segment depletion layer at the inclusion-polymer interface. The accompanying increase in free volume leads to a significant increase in the local penetrant diffusivity, which, in turn, increases the bulk permeability and selectivity.