We consider within a modified Poisson-Boltzmann theory an electrolyte, with different mixtures of NaCl and NaI, near uncharged and charged solid hydrophobic surfaces. The parametrized potentials of mean force acting on Na+, Cl-, and I- near an uncharged self-assembled monolayer were deduced from molecular simulations with polarizable force fields. We study what happens when the surface presents negative charges. At moderately charged surfaces, we observe strong co-ion adsorption and clear specific ion effects at biological concentrations. At high surface charge densities, the co-ions are pushed away from the interface. We predict that Cl- ions can also be excluded from the surface by increasing the concentration of NaI. This ion competition effect (I- versus Cl-) may be relevant for ion-specific partitioning in multiphase systems where polarizable ions accumulate in phases with large surface areas.