We report Monte Carlo simulation results for double layers of 1:1 and 2:1 electrolytes near an electrode with an inner layer that has a dielectric constant, 62, smaller than that of the electrolyte, epsilon(3). The electrolyte is modeled in the implicit solvent framework (primitive model), while the electrode is a metal electrode in this study (epsilon(1) -> infinity). The charged hard sphere ions are not allowed to enter into the inner layer. We show that the capacitance of the inner layer is C-delta = epsilon(0)(epsilon(2) + epsilon(3))/2 delta, where delta is the thickness of the inner layer. This result is different from that obtained from solutions of the Poisson-Boltzmann equation (epsilon(0)epsilon(2)/delta), indicating that interpretation of experimental data with a fitted epsilon(2) dielectric constant of the inner layer must be done using a different equation. We also show that the properties of the diffuse layer are not independent of the value of epsilon(2), which is a usual assumption of the Poisson-Boltzmann theory. This is mainly because the repulsive image charges repel both the counterions and the co-ions, while the electrode charge attracts the counterions and repels the co-ions.