We have performed (N,V,T) Monte Carlo simulations in order to study the stability of two parallel charged surfaces (lamellae) neutralized by exchangeable counterions. By varying each parameter characterizing the interface, i.e., the interlamellar separation, the surface charge density of the lamellae, the dielectric constant of the solvent, and the radius and charge of the counterions, we have determined the stability of a wide class of physical situations. The ion-ion, lamella-ion, and lamella-lamella interactions are described within the context of the "primitive model". We give evidence that, despite the intrinsic simplicity of the primitive model, the phase diagram of such a system exhibits complex patterns. We have determined 2D contour maps of the equation of state in order to localize attracto/repulsive domains and optimize adhesive properties of the interface. This study concerns a large variety of lamellar materials, including hydrated cement and clays, and pillared and organo clays. At low dielectric constant, we have also found evidence of an attractive regime for lamellae neutralized by monovalent counterions.