A lattice-gas model is used to investigate the specific adsorption of ions at the interface between two immiscible electrolyte solutions. From Monte Carlo simulations, the profiles of particle densities and of the electrostatic potential are obtained. Specific adsorption is shown to affect the potential distribution markedly. In some cases an overshoot of the potential can be observed, an effect that is well known from specific adsorption at metal electrodes. This redistribution of charge and potential can increase the interfacial capacity, shift the potential of zero charge, and influence the rate of electron-transfer reactions.