We present an analytical model of salt- and water-ion transport across an ion-selective interface based on an assumption of local equilibrium of the water-dissociation reaction. The model yields current-voltage characteristics and curves of water-ion current versus salt-ion current, which are in qualitative agreement with experimental results published in the literature. The analytical results are furthermore in agreement with direct numerical simulations. As part of the analysis, we find approximate solutions to the classical problem of pure salt transport across an ion-selective interface. These solutions provide closed-form expressions for the current-voltage characteristics, which include the overlimiting current due to the development of an extended space-charge region. Finally, we discuss how the addition of an acid or a base affects the transport properties of the system and thus provide predictions accessible to further experimental tests of the model.