Nonlinear Poisson-Boltzmann theory is developed to extend our previous work [Phys. Rev. E 53, 6192 (1996)] on the case when the potential drop across the double layer is not small compared to the thermal energy. Close to the potentials of zero charge (pzc) the effect of surface roughness on the double-layer capacitance is mainly determined by an interplay between the lateral correlation length of roughness and the Debye length. However, far from the pzc dramatic effects of electrode potential are found which are not reduced to the potential-induced shortening of the diffuse layer thickness.