We apply the classical over-the-barrier (COB) model to charge transfer between highly charged ions (HCIs) and targets consisting of thin dielectric films on metals. Distances for the onset of classically allowed above-surface electron capture are obtained as a function of HCI charge state, film thickness, film permittivity, and film-metal electron binding energies. The model describes the crossover between the previously existing COB model for bulk metals and bulk dielectrics as the thickness of a dielectric film on a metal substrate increases through three distinct regimes. For ultrathin films with low permittivity and positive electron affinity, over-the-barrier charge transfer initiates from the metal electrons behind the film and critical distances are greater than those from bare metal targets. This result is consistent and compared with the recent observation of potential emission enhancement above thin C60 films on Au(111) with increasing film thickness.