Bipolar membranes are layered structures composed of one cation-and one anion-exchange membrane joined together in series. The current-voltage curves of two recently developed bipolar membranes have been analysed theoretically and experimentally under both forward and reverse bias conditions. The experimental trends observed are high conductivity under forward bias conditions and high impedance first, and then electric field enhanced (EFE) water dissociation for high enough applied voltages, under reverse bias conditions. The forward bias measurements can contribute to a better knowledge of some of the transport parameters entering also in the reverse biased membrane. Comparison of experiment with a theory based on the Nernst-Planck and Poisson equations allows for further testing of the theoretical model successfully employed previously for the case of the reverse biased membrane, and gives new support to the hypothesis that an EFE water dissociation reaction involving the membrane fixed groups in the bipolar junction is responsible for the breakdown of the current saturation regime observed under reverse bias conditions.