We have studied by X-ray reflectometry the variation of electron density of thin polymer films near solid substrates. For most polymers studied, which interact only mildly with the selected substrate (SiO2), a decrease of density was detected over a region spanning two to three statistical segment lengths at the solid interface. For poly(4-vinylpyridine) (P4VP), however, an increase of density was observed. This is related to the existence of strong adsorption interactions between P4VP and SiO2. These observations are in good agreement with theoretical predictions and may play a role in explaining the variation of the glass transition of thin supported polymer films as compared to bulk glass transitions.