A perturbation analysis is applied to a nonequilibrium double electric layer (NDEL) near a membrane with extended soft permeable interfaces (polar zones) under steady-state ion flux conditions. The membrane has been modeled as composed of three layers : an inner hydrophobic layer and two polar zones with fixed charges and dipoles. Ion flux is described according to Nernst-Planck and Poisson equations, A first order approximation of the nonequilibrium electric potential has been obtained, using the electric current as the small parameter. The influence of the ionic flux, the surface dipole density, and the thickness of the polar zone on the NDEL near the membrane has been analyzed. The electric potential and hence the ion concentration profiles in the NDEL change considerably with surface dipole density. A maximum in the electric potential, which is determined by ion flux and polar zone parameters, is predicted in certain cases. The effects shown can help in the interpretation of permselectivity measurements.