A membrane with soft permeable interfaces in an aqueous solution has been modelled by taking into account the spatial distribution of structural electric charges and dipoles in the interfaces. The model was developed with special stress on its application to biological membranes. The electric potential distribution and the ion transport across the membrane are studied and the important role of the interface thickness L on ion transport and membrane selectivity is shown. An interesting result is found for certain combinations of charge and dipole densities : a cation selective membrane may become anion selective when L changes. It is discussed how the results obtained can help to explain experimental results for membrane selectivity.