We have studied the growth of the wetting layer formed at the surfaces of symmetric and nonsymmetric mixtures of poly(ethylenepropylene) (PEP) and perdeuterated poly(ethylenepropylene) (dPEP) during spinodal decomposition. For off-critical quenches, the growth rate is found to be strongly dependent on the bulk composition of the mixtures. If the minority phase wets the surface, the wetting layer is found to grow slower than in the reverse situation, where the majority phase wets the surface. In the latter case, hydrodynamic effects may play a role, increasing the rate of wetting layer growth. The surface spinodal waves are shallower for the case of off-critical compositions as compared to critical compositions. However, independent of bulk composition, all surface composition profiles exhibit universal scaling behavior in the near-surface region. Our conclusions are strengthened by numerical simulations of a diffusively coarsening mixture near a surface that attracts one of the phases, No appreciable acceleration of growth of the surface layer is observed in simulations where the wetting phase is the majority phase, suggesting that the acceleration observed experimentally is due to fluid flow. The simulations also show that there can be "surface-induced nucleation" in the case that the majority phase is attracted by the substrate : the expulsion of minority phase can lower the nucleation barrier near the substrate, causing more droplets to nucleate there than in the bulk.