We use grand canonical Monte Carlo simulations in the framework of the primitive model to determine the mechanical stability of planar charged interfaces in the presence of various salts of multivalent counterions. Our intent is to determine the influence of salt addition on the strength and the range of interionic correlations. Despite the simplicity of the primitive model, the equation of state of these interfacial systems exhibits complex behavior because the addition of salts of di- and trivalent counterions enhances the interionic correlations and induces the coexistence of two phases composed of differently swollen interfaces. The occurrence of such phase coexistence is related to the inversion of the apparent interfacial charge and the accumulation of salt in the interfacial domain by contrast with the Donnan exclusion phenomenon.