Recent theory of capillary waves along the interface between two immiscible electrolytes is generalized to include the non-linear polarization of the double layer. The theory covers both the effects of the capillary waves on the double layer capacitance, as well as the effect of charging the interface on the amplitudes and spectrum of capillary waves. The theory explains major available experimental data, such as the interfacial capacitance dependence on the potential drop across the interface and on ionic strength. It also predicts a number of new effects, such as the influence of electric field and electrolyte concentration on the surface corrugation correlation function, and in particular, on the mean square height of corrugation.