The electrical and optical properties of ultrathin films of tetragonal barium titanate (BaTiO₃) on strontium titanate (SrTiO₃) single-crystal substrates are theoretically investigated using a microscopic quantum mechanical model based on the orbital approximation in correlation with the dipole-dipole interaction. First-, second-, and third-order electronic polarizabilities had to be considered in this calculation in order to obtain accurate results for both the dielectric spontaneous polarization and the refractive indices of the BaTiO₃ overlayer. The spontaneous polarization is drastically reduced in the film as its thickness decreases. However, an electronic polarization appears within the SrTiO₃ substrate in the neighbourhood of the interface. This polarization, which vanishes far away from the interface into the SrTiO₃ bulk, is induced by the polarization of the BaTiO₃ film. Furthermore, we find the refractive index for both the BaTiO₃ film and the SrTiO ₃ substrate to be deeply reduced for light polarized perpendicular to the surface.