In this experimental study, the influence of asymmetric bipolar membranes on the salt impurities in the acid and base product is investigated. The thickness of one, the other, or both ion-permeable layers of a bipolar membrane is increased. With increased layer thickness, the current-voltage curves of the electrodialysis repeat unit recorded in a pilot-scale module show a reduced limiting current density, and thus they indicate an overall higher selectivity of these arrangements. Furthermore, these curves indicate water transport limitations for some membrane arrangements. Electrodialysis experiments with the same module at a high current density confirm the overall salt ion flux reduction. Moreover, these acid-base electrodialysis experiments directly reveal an increased asymmetry of the salt ion fluxes which can be utilized to design custom-made bipolar membranes with very high purity of either the produced acid or the base while keeping the bipolar membrane functioning without water transport limitations. The presented experiments also show that the bipolar membrane behavior can be characterized in situ, i.e., as a part of a electrodialysis repeat unit mounted in a pilot-scale electrodialysis module.