Diffusion within polymer electrolyte membranes is often coincident with time-dependent processes such as swelling and polymer relaxation, which are factors that limit their ability to block molecular crossover during use. The solution-diffusion model of membrane permeation, which is the accepted theory for dense polymers, applies only to steady-state processes and does not address dynamic internal structural changes that can accompany permeation. To begin discovery of how such changes can be coupled to the permeation process, we have constructed a stochastic multiscale reaction-diffusion model that examines time-dependent methanol uptake into and swelling of hydrated Nafion. Several potential mechanisms of diffusion and polymer response are tested. The simulation predictions are compared to real-time Fourier transform infrared attenuated total reflectance spectroscopy (FTIR-ATR) absorbance reported in the literature [Hallinan, D. T., Jr.; Elabd, Y. A. J. Phys. Chem. B 2007, 111, 13221-13230]. Of the proposed polymer response mechanisms, only one, a reaction-limited, local response to increasing methanol concentration that takes the entire experimental time frame of 600 s, produces simulated FTIR-ATR data consistent with experiment. The simulations show that water diffusion out of the membrane is minimal during methanol sorption and that changes in the measured infrared absorbances are due primarily to the increase in methanol concentration accompanied by dilution of water during swelling. Swelling involves densification of the polymer structure even as there is an overall volume expansion of the film. Potential connections between the polymer densification and molecular-level structural changes of Nafion in methanol are discussed. These results indicate that the interaction between methanol and Nafion serves to increase Nafion's capacity to accommodate large volumes of methanol-water solutions, facilitating increased permeation across the membrane relative to pure water.