In this Brief Report, we perform molecular-dynamics simulations of an interface containing charged functional groups of different valences in contact with 2:1 ionic solution. We take into account both the finite sizes of the ions in solution and the functional groups but we neglect the structural details of the solvent (primitive model). We show that the interaction between a charged interface (of given surface charge density) and electrolyte depends strongly on the individual charges of the interfacial groups originating the surface charge. In particular, we show that charge inversion (i.e., interfacial charges attracting counterions in excess of their own nominal charge) is enhanced by the presence of multivalent interfacial groups (such as certain phospholipids). Overall, our results reveal that in primitive models of the ion-interface interaction not only the ionic size and valence are important but also the size and valence of the interfacial charged groups have a significant impact.