Extremely thin films of poly(styrene) (h <= 6 nm), in the geometry of "model" nanocomposites, show a continuous increase of the capacitance with temperature. This phenomenon is discussed in terms of a gradual defreezing of the interfacial zone between the so-called dead layer and the bulk. Such a mechanism shows a strong analogy to the dielectric response of the rigid amorphous fraction in semicrystalline materials. The defreezing process, foregoing the dynamic glass transition, is responsible for the temperature dependence of the deviations from bulk behavior.