The dielectric response of a ferroelectric film with bilinear coupling between order parameter and strain is theoretically addressed. An exact solution for the total (lattice and domain contributions) dielectric permittivity of the system for the case where the domain spacing is much smaller than of film thickness is reported. An unusual temperature dependence of the permittivity in the polydomain state is found: it stays constant below the phase transition. The treated problem has been found to be a remarkable case where the choice of the order parameter between two linearly coupled variables is crucial.