Solid/liquid interfaces can acquire a charge by two principally different processes, i.e., by charging the interface via an external electric source or by specific adsorption/desorption of ionic species from/to the liquid. Here, we analyze the properties of electric double layers (DL) that are governed by the simultaneous functioning and coupling of these two charging mechanisms. For such interfaces, which we will denote as amphifunctional, the quantitative dependencies of the DL parameters on the electric variables and bulk composition are computed. The interface between a partially oxidized metal and an electrolyte solution is an example of an amphifunctional interface. Particular situations occur at the point of zero charge (pzc) and at the isoelectric point, which refer to specific values of the electrode potential and the pH of the solution. Limiting cases of the amphifunctional model correspond to the familiar DL behavior of either fully polarized metal/electrolyte interfaces or fully relaxed oxide/electrolyte interfaces. Our analysis can successfully be applied in the interpretation of recent atomic force microscopy force measurements on the gold/solution interface. It also allows a new approach in the understanding of the dependence on pH of the potential of zero charge of metals and the dependence on the potential of pzc (pH value) of oxide surfaces.