The nonlinear Poisson-Boltzmann model is used to derive analytical expressions for the free energies of both mixed anionic-zwitterionic and mixed cationic-zwitterionic lipid membranes as function of the mole fraction of charged lipids. Accounting explicitly for the electrostatic properties of the zwitterionic lipid species affects the free energy of anionic and cationic membranes in a qualitatively different way: That of an anionic membrane changes monotonously as a function of the mole fraction of charged lipids, whereas it passes through a pronounced minimum for a cationic membrane.