The aim of this contribution is to propose a non-linear model for describing the isothermal mass transport of a solvent into an immiscible polymeric blend embedding an internal interface, under and in the absence of flow. The blend internal structure (interface + conformation) is characterized, by two symmetric second-order tensors A and m describing, respectively, the local changes occurring at the interface and in the polymer conformation. The governing equations, derived on a mesoscopic level of description and possessing the general equation for the non-equilibrium reversible and irreversible coupling (GENERIC) structure, explicitly incorporate the coupling arising between the deformation, flow, and diffusion. In the absence of flow, the model extends Fick's laws and provides a mathematical framework for describing non-Fickian diffusion. Particular cases of the model are also discussed, and both linear dispersive and non-linear hyperbolic wave propagation of disturbances in the solvent concentration are examined. Formulas for the characteristic speed, phase velocity, and attenuation are also calculated.