Capacitors in electrical and electronic systems composed of thin film dielectrics operate under extremely high electric fields. Dynamics of charge transport and relaxation are closely correlated to the energy storage properties and electrical degradation of thin film dielectrics for capacitive applications. In this paper, the dielectric relaxation properties of poly (vinylidene fluoride-hexafluoropropylene) (P(VDF-HFP)) copolymer films are investigated over a broad frequency range from 10 mHz to 10 MHz and temperature range from -130 °C to 130 °C. The dielectric responses correlated to bulk and interfacial processes are clarified by varying the thickness and interfacial contact status of P(VDF-HFP) films. A low frequency process originating from the quasi-DC (QDC) process and a dielectric dispersion process correlated to the interfacial polarization are identified based on the Dissado-Hill dielectric response model and the equivalent circuit analysis. The high permittivity and high operation electric field of P(VDF-HFP) for capacitive energy storage give rise to improved blocking capacitance associated with the interface, suggesting the enhanced interfacial polarization. This work provides insights into the bulk and interface charge dynamics of polymer thin film dielectrics.