The interaction of two parallel lipid membranes in an electrolyte solution at physiological conditions is considered. Each lipid layer facing the aqueous solution is modeled as a planar surface of dielectric discontinuity at the hydrocarbon/water interface. The headgroup structure of zwitterionic lipids is modeled as a two-dimensional dipolar liquid at this surface. According to recent theoretical studies of membrane structure and macroion adsorption [1, 2, 3], this model succeeds in explaining the major structural and electrostatic properties of membranes. In our work we study the effect of the zwitterionic lipid headgroup structure on the electrical double layer formed upon lipid membranes, the anisotropic correlations between ions and lipids, and interactions. We generalize the anisotropic reference hypernetted chain (ARHNC) theory [4] to the case of inhomogeneous fluids near surface with structured charge: the ARHNC equations are modified to include a two-dimensional liquid layer of linear (dipolar) molec