In view of efficient and nontoxic delivery of genes to cells, complexes made of phospholipids (noncationic) and DNA are assembled through the mediation of multivalent cations. The association of lipids with DNA is explained through the charge reversal of lipid headgroups by specific adsorption of cations. The ion binding is quantified by the Gouy-Chapman-Stern theory which provides a good estimate for the minimal concentration of cations required to produce complexes. Coarse-grained Monte Carlo calculations support X-ray diffraction experiments in the sense that lipids form inverted micelles around hexagonally arranged DNA rods, with cations in between to maintain the cohesion. The complexes are more cohesive in terms of total free energy as the cation valence increases. The presented methodology may help develop predictive models for biomolecular self-assembled systems.