The Gouy-Chapman-Stern model (GCS) has been extended to the case of the metal-solid electrolyte interface in which the positions of charges in the electrolyte are discrete. Our model allows mobile positive and negative charges to move freely parallel to the metal electrode surface, but constrains the charges to lattice planes at fixed distances Ax, 2A.x. 3Ax etc. normal to the metal surface. The non-linearised Poisson-Boltzmann equation for this system was solved to compute the potentials and charges on each plane and interfacial capacitance-potential curves (C,,,_ -E) were constructed. We compare these C,,,,-E curves with those predicted by the GCS model. Significant deviations from GCS were found when the condition &A.&,, < I was not satisfied. Here k is the reciprocal of the Debye Length, Ax is the lattice plane spacing and 0,) ( = Fc#+,/RT) is the normalised interfacial potential drop (&). The condition kA.x -=z 1 was not sufficient because at large 0,, the charge decays more rapidly with distance than the potential and effects of discretisation are still observed. The single mobile carrier case was treated and good agreement with the Mott-Schottky depletion layer approximation was obtained. We have also treated cases in which there is a limit to the amount of charge which can be accommodated on a single lattice plane; the effect of this restriction is to introduce a maximum in the C,,-E curve as the potential is moved away from the potential of zero charge. Incorporation of a disordered and therefore active first layer in which the density of carriers is larger than in the bulk results in the 'washing out' of the diffuse layer minimum. The model was extended to include specific adsorption of anions in a plane halfway between the metal surface and the first lattice plane. When charge occupancy of the planes was allowed to reach high values ( > 10 pC cm-*) the C,, -E curve shows oniy a transition between two Helmholtz-like capacitances. Restricting the charge occupancy on the planes results in a peak in the C,,-E curve at a potential determined by the free energy of adsorption and a positive shift in the potential of the diffuse layer minimum. This shift disappears as the charge occupancy on the planes is decreased further.