Modeling electrostatic properties of macroions such as charged lipid membranes is especially simple within linear Debye-Hückel theory where analytical solutions are often available. Charged lipid layers typically also contain zwitterionic lipids that possess a large headgroup dipole. We incorporate the presence of zwitterionic lipids into the Debye-Hückel description and derive analytical expressions for the free energies of isolated and interacting lipid layers. Our approach accounts for two major characteristic features of zwitterionic lipids, the firm linkage of the dipole's negatively charged phosphate end to the lipid chain and the comparatively large conformational freedom of the opposite, positively charged, dipole end. This leads to differences in structural properties of mixed anionic and cationic lipid layers that are known from experiment and that the Debye-Hückel description qualitatively recovers. Most notably, this includes the different dependencies of the average cross-sectional area per lipid on the composition of mixed anionic and cationic membranes. In addition, we study the predictions of Debye-Hückel theory regarding the electrostatic influence of zwitterionic lipids on the stability of non-ideally mixed membranes as well as on the adsorption energy of oppositely charged macroions.