The charged capillary model for microporous membranes has been extended to account for a distribution of fixed charge transversal to the pore wall. The non-linearized Poisson-Boltzmann equation has been solved numerically and results obtained for an exponential charge distribution function have been analyzed. The expressions used for computing the streaming potential and the pore conductivity arise from Poisson-Boltzmann equation together with Nernst-Planck and Navier-Stokes equations. The effect of charge displacement on streaming potential and wall potential is significant, especially for high bulk electrolyte concentration, unlike Pore Conductivity which slightly changes with respect to the case of charge smeared at the pore wall. The model is expected to be useful for microporous membranes whose pore dimensions are very small, and also for some membrane-like biological systems. In particular, this transverse-charge model could be used in the study of electrokinetic phenomena through human Stratum Corneum, provided fixed charge density and "pore" dimensions are known.