Universal aspects of the charge transport through strongly disordered potential barriers in metallic heterojunctions are analyzed. A simple theoretical formalism for two kinds of transmission probability distribution functions valid for smooth tunneling barriers and those with abrupt boundaries is presented. We argue that their universality has simple mathematical origin and can arise in totally different physical contexts. Finally, we analyze possible applications of superconducting junctions to test the universality of transport characteristics in structurally disordered insulating films without any fitting parameters and point out that the proposed approach can be useful in understanding the dynamics of surface screening currents in superconductors with an inhomogeneous near-surface region. (C) 2014 Elsevier B.V. All rights reserved.