Diffusion, coupled with rheology, of a simple fluid through a complex polymeric membrane is modeled using the Poisson and dissipation bracket formalism. A set of governing equations describing the time evolution of concentration, flux, and internal structure of the complex polymeric membrane is obtained. Two parameters, which characterize the importance of elasticity and mixing properties, appear in the governing equations. An extension of Fick's second law is derived for the flux evolution. The model describes the diffusion process quantitatively quite well.