We develop a nonlinear theory for the calculation of interfacial structural properties of a dipolar mixture in contact with a charged solid surface. Both the molecular sizes and the dipole moments of various species can be unequal. Explicit numerical results are obtained for the interfacial structure of a binary dipolar liquid in contact with a charged surface of varying surface charge density. The dipole moments of the two species are also varied. The density profiles of both the species are found to be highly inhomogeneous and oscillatory near the solid surface. The more polar species is found to exhibit a positive electrostriction at the surface with an increasing surface electrostatic field. An opposite behavior is observed for the less polar species. The polarization profiles reveal pronounced orientational order of the solvent molecules of both the species near the charged surface. The contact polarizations of the more polar and the less polar species show, respectively, a more than linear and a less than linear increase with increasing surface charge density. The predictions of the present theory for a given set of parameter values are compared with the results of Monte Carlo simulation of the same system and a good agreement is found for the inhomogneous density and polarization profiles of both the species.