The increasing interest in charge transport across amorphous nanometer‐thick oxide layers is motivated by their promising applications in semiconductor and superconductor electronics. But usually, electrical characteristics of corresponding devices strongly differ from those following from a conventional theory of tunneling processes. In this work we discuss a possible reason of the anomalous behavior, namely, the presence of an universal bimodal distribution of transparencies across ultra‐thin insulating films. We present low‐temperature current‐voltage characteristics of tunnel junctions with superconducting MoRe alloy electrodes separated by an inhomogeneous nano‐scaled interlayer and found a good agreement between experimental data and numerical results of our theoretical approach.