Divalent cations, i.e., calcium, magnesium, and others, are able to enhance the ability of DNA to interact with membranes that are composed of zwitterionic lipids such as phosphatidylcholine. The resulting condensed complexes offer potential applications as nontoxic gene delivery vehicles. The present study suggests a generic theoretical model to describe the energetics and structural features of a zwitterionic lipid-DNA complex in the presence of divalent cations. Specifically, we consider the adsorption of a single molecule of double-stranded DNA onto a planar zwitterionic lipid layer. Our theoretical model is based on the continuum Poisson-Boltzmann formalisms, which we modified so as to account for the two opposite charges and orientational freedom of the zwitterionic lipid headgroups. We find a substantially more favorable adsorption free energy of the DNA if divalent cations are present. In addition, our model predicts the divalent cations to preferentially interact with the phosphate groups of the zwitterionic lipids, given these lipids are located in close vicinity to the DNA. This is accompanied by a small but notable reorientation of the zwitterionic headgroups toward the DNA. We demonstrate that the binding of DNA onto a zwitterionic lipid layer is not driven by the release of counterions. Instead, the binding leads to a partial redistribution of the divalent cations, from the phosphate groups of the DNA (prior to the binding) to the phosphate groups of the zwitterionic lipids (after the binding). Our results thus suggest a general physical mechanism underlying complex formation between DNA and zwitterionic lipids in terms of mean-field electrostatics, i.e., neither involving correlations nor specific interactions of the divalent cations.