Finite element simulations were used to investigate the effect of a smooth variation of permittivity across a polarized liquid/liquid interface on the differential capacitance. The results show that a relative permittivity profile can account for the variation of ion solvation in the interfacial region, and therefore upon the diffuse double layer itself. The width and the symmetry of this profile across the interface are shown to be crucial parameters for interfacial distributions and fitting of capacitance data has been used to estimate the width of the interfacial region.