The interaction of two oppositely charged surfaces has been investigated using Monte Carlo simulations and approximate analytical methods. When immersed in an aqueous electrolyte containing only monovalent ions, two such surfaces will generally show an attraction at large and intermediate separations. However, if the electrolyte solution contains divalent or multivalent ions, then a repulsion can appear at intermediate separations. The repulsion increases with increasing concentration of the multivalent salt as well as with the valency of the multivalent ion. The addition of a second salt with only monovalent ions magnifies the effect. The repulsion between oppositely charged surfaces is an effect of ion-ion correlations, and it increases with increasing electrostatic coupling and, for example, a lowering of the dielectric permittivity enhances the effect. An apparent charge reversal of the surface neutralized by the multivalent ion is always observed together with a repulsion at large separation, whereas at intermediate separations a repulsion can appear without charge reversal. The effect is hardly observable for a symmetric multivalent salt (e.g., 2:2 or 3:3).