The success of perovskite solar cells has sparked enormous excitement in the photovoltaic community not only because of unexpectedly high efficiencies but also because of the future potential ascribed to such crystalline absorber materials. Far from being exhaustively studied in terms of solid-state properties, these materials surprised by anomalies such as a huge apparent low-frequency dielectric constant and pronounced hysteretic current-voltage behavior. Here we show that methylammonium (but also formamidinium) iodoplumbates are mixed conductors with a large fraction of ion conduction because of iodine ions. In particular, we measure and model the stoichiometric polarization caused by the mixed conduction and demonstrate that the above anomalies can be explained by the build-up of stoichiometric gradients as a consequence of ion blocking interfaces. These findings provide insight into electrical charge transport in the hybrid organic-inorganic lead halide solar cells as well as into new possibilities of improving the photovoltaic performance by controlling the ionic disorder.