Recently we derived an extension to the linear Gouy-Chapman theory, in order to describe the properties of a modulated liquid \ liquid interface between two immiscible electrolyte solutions. In this work we extend our approach to include specific adsorption of tons at the interface. Starting from a Hamiltonian which contains a singular part for the surface contributions, we obtain, within the mean-field approach, a set of equations which allows us to study the equilibrium between the diffuse and the singular part of the charge earners. It is shown that both adsorption and the roughness of the interface lead to a higher capacity compared with the prediction of the Gouy-Chapman theory. The correction introduced by the perturbation from a flat geometry involves the interplay beta een the two-point height-height correlation function of the surface, the Debye lengths of the system, and a length characterizing the adsorption. Furthermore, we investigate the equilibrium distribution of an excess charge into an adsorbed and a diffuse part and show that the interface modulation shifts this equilibrium towards the adsorbed charge.