A two-scale theory for the swelling biopolymeric media is developed. At the microscale, the solid polymeric matrix interacts with the solvent through surface contact. The relaxation processes within the polymeric matrix are incorporated by modeling the solid phase as viscoelastic and the solvent phase as viscous at the mesoscale. We obtain novel equations for the total stress tensor, chemical potential of the solid phase, heat flux and the generalized Darcy's law all at the mesoscale. The constitutive relations are more general than those previously developed for the swelling colloids. The generalized Darcy's law could be used for modeling non-Fickian fluid transport over a wide range of liquid contents. The form of the generalized Fick's law is similar to that obtained in earlier works involving colloids. Using two-variable expansions, thermal gradients are coupled with the strain rate tensor for the solid phase and the deformation rate tensor for the liquid phase. This makes the experimental determination of the material coefficients easier and less ambiguous.