Neutron reflection (NR) and spectroscopic ellipsometry (SE) were used for the investigation of the interfaces between films of poly(vinyl methyl ether) (PVME, glass transition temperature (T-g) = -31 degrees C) and polystyrene (PS, T-g similar to 105 degrees C). The transport of PVME into PS at temperatures below the glass transition of PS was highly non-Fickian. The linear dependence of the front propagation with time, along with the high activation energy for transport indicates some similarities to classical case II transport of solvent into polymer glasses. The variation of PVME transport rate with PS molecular weight (MW) illustrates one significant difference as compared to classical case II transport. The strong dependence of PVME transport rate on PS MW is attributed to the MW dependence of the rate of swelling and dissolution of PS in the swollen front region. It was also found that the transport rate (front velocity) of PVME into PS depended strongly on the temperature and time of preannealing of the single spin coated PS layer. Preannealing at temperatures well above T-g for higher MW PS films was necessary. Birefringence measurements on PS films proved that internal stress was not a factor. A systematic MW study indicated that the major factor was the reduced entanglement density due to spinning of PS films from solution.