The relative permittivity = epsilon/epsilon(0) of thin films used in organic electronic devices is directly related to the structure and the molecular polarizability when intermolecular overlap is small. Monolayer and multilayer films are modeled as lattices of polarizable points with induced dipoles = F where the internal electric field F includes contributions from all induced dipoles. The polarization per unit volume is P = n for number density n. Dipole-field sums are evaluated directly for atomic and molecular crystals and films through stacking of infinite layers. Lorentz factors in uniformly polarized crystals of less than cubic symmetry resolve completely the conditional convergence of dipole-field sums in three dimensions. Thin films have equal P within layers but not at or near the surface. Surface effects are shown to increase with n and sometimes to extend into films even though dipole fields are mainly due to adjacent layers. Simple and body-centered tetragonal lattices illustrate polarizing or depolarizing interactions between layers that mimic molecules or oligomers tilted at angle phi from normal to the surface in films or SAMs. Uniform P in molecular films refers to unit cells rather than to atoms and there are multiple ways to partition anisotropic molecular among polarizable points. An illustrative analytical model based on polarizable points and dipole fields of adjacent layers is applied to oligophenyl films and to conjugated molecules in acene films.