We performed neutron reflectivity measurements on multilayered polymer thin films consisting of alternatively stacked deuterated polystyrene (d-PS) and hydrogenated polystyrene (h-PS) layers similar to 200 angstrom thick as a function of temperature covering the glass-transition temperature T(g), and we found a wide distribution of T(g) as well as a distribution of the thermal expansivity a within the thin films, implying the dynamic heterogeneity of the thin films along the depth direction. The reported anomalous film thickness dependences of T(g) and alpha were reasonably understood in terms of the distributions, showing that the surface mobile layer and the bottom hard interfacial layer are, respectively, responsible for the depressions of T(g) and alpha with decreasing film thickness. The molecular mobility in each layer is also discussed in relation to the distribution of T(g), based on the results on mutual diffusion at the layer interface.