Nanoindentation measurements of the elastic moduli E-r of thin polymer films supported by stiff substrates with moduli E-s >> E-r show an increase of Er with decreasing h, for h less than a threshold thickness h(t). In the thickness range h < h(t), the value of the modulus manifests the influence of various interactions associated with the "stiff" substrate. We show that h, is a function of composition for the miscible blend of polystyrene (PS) and tetramethyl bisphenol-A polycarbonate (TMPC). The modulus E-r,(TMPC) of TMPC films supported by SiOx increases for h < h(t)(TMPC) similar to 300 nm while h(t)(PS) similar to 450 nm for the modulus E-r,E-PS of PS films, supported by the same substrate. The threshold thicknesses of the blends and the moduli of the blends appear to be reasonably described by an effective medium approximation. This behavior is rationalized in terms of the vibrational force constants f, determined using incoherent neutron scattering experiments, of the materials.