We develop a statistical thermodynamic model for the phase evolution of DNA-cationic lipid complexes in aqueous solution, as a function of the ratios of charged to neutral lipid and charged lipid to DNA. The complexes consist of parallel strands of DNA intercalated in the water layers of lamellar stacks of mixed lipid bilayers, as determined by recent synchrotron x-ray measurements Elastic deformations of the DNA and the lipid bilayers are neglected, but DNA-induced spatial inhomogeneities in the bilayer charge densities are included. The relevant nonlinear Poisson-Boltzmann equation is solved numerically, including self-consistent treatment of the boundary conditions at the polarized membrane surfaces. For a wide range of lipid compositions, the phase evolution is characterized by three regions of lipid to DNA charge ratio, rho: 1) for low rho, the complexes coexist with excess DNA, and the DNA-DNA spacing in the complex, d, is constant; 2) for intermediate rho, including the isoelectric point rho = 1, all of the lipid and DNA in solution is incorporated into the complex, whose inter-DNA distance d increases linearly with rho; and 3) for high rho, the complexes coexist with excess liposomes (whose lipid composition is different from that in the complex), and their spacing d is nearly, but not completely, independent of rho. These results can be understood in terms of a simple charging model that reflects the competition between counterion entropy and inter-DNA (rho < 1) and interbilayer (rho > 1) repulsions. Finally, our approach and conclusions are compared with theoretical work by others, and with relevant experiments.