The bipolar membrane or double fixed charge membrane (DFCM) consists of a central depletion layer of low conductivity surrounded by outer regions of high conductivity. The Nemst-Plank-Poisson equations for alternating currents are solved for each region separately with appropriate approximations. The two solutions are melded to give the solution for the membrane as a whole. The results are presented as the frequency dependence of the relevant capacitance and conductance. At the low and high frequency limits these parameters become independent of frequency, with a monotonic dispersion at intermediate frequencies in agreement with observation. The dispersion is interpreted in terms of the alternating electric field which is confined to the depletion layer at low frequency but is almost uniform through the entire membrane at high frequency. The dispersions are similar to those of a two element Maxwell-Wagner system, but the elements required for the latter may not be identified with the separate regions of the DFCM.