We consider the electrostatic interaction between two rigid membranes, with
different surface charge densities of opposite sign, across an aqueous sol
ution without added salt. Exact solutions to the nonlinear Poisson-Boltzman
n equation are obtained and their physical meaning discussed. We also calcu
late the electrostatic contribution to the free energy and discuss the reno
rmalization of the area per head group of the charged lipids arising from t
he Coulomb interaction.