We report the effect of "interactive" polymer network (PN) supports on the solvent-vapor processing of thin polymer films. Densely cross-linked surface-attached network exhibits under experimental time scale a glassy swelling behavior with the conformational states and solvent uptake clearly sensitive to the degree of solvent vapor saturation in the atmosphere. Pretreatment of the thermally cured PN films by complete immersion or by swelling in saturated chloroform vapors facilitates relaxation of the residual stresses and induces irreversible changes to the network structure as revealed by the swelling/deswelling tests. The presence of a polymer film on top of the PN support results in a mutual influence of the layers on the respective swelling kinetics, steady-state solvent uptake, and chain dynamics. Using UV-vis ellipsometry, we revealed a significantly faster swelling and higher solvent uptake of glassy PN layer below a polymer film as compared to a single PN layer on silicon substrate. Remarkably, the swelling of the network support continues to increase even when the overall swelling of the bilayer is in a steady-state regime. Block copolymer films on PN supports exhibit a faster ordering dynamics and exceptional stability toward dewetting as compared to similar films on silicon wafers. The mechanical stress produced by continuously swelling PN is suggested to account for the enhanced segmental dynamics even at low solvent concentration in the block copolymer film. Apart from novel insights into dynamics of solvent uptake by heterogeneous polymer films, these results might be useful in developing novel approaches toward fast-processing/annealing of functional polymer films and fibers.