We present a theoretical study of the physical properties of cationic lipid-DNA (CL-DNA) complexes - a promising synthetically based nonviral carrier of DNA for gene therapy. The study is based on a coarse-grained molecular model, which is used in Monte Carlo simulations of mesoscopically large systems over timescales long enough to address experimental reality. In the present work, we focus on the statistical-mechanical behavior of lamellar complexes, which in Monte Carlo simulations self-assemble spontaneously from a disordered random initial state. We measure the DNA-interaxial spacing, dDNA, and the local cationic area charge density, σM, for a wide range of values of the parameter φc representing the fraction of cationic lipids. For weakly charged complexes (low values of φC), we find that dDNA has a linear dependence on φc-1, which is in excellent agreement with x-ray diffraction experimental data. We also observe, in qualitative agreement with previous Poisson-Boltzmann calculations of the system, large fluctuations in the local area charge density with a pronounced minimum of σM halfway between adjacent DNA molecules. For highly-charged complexes (large φc), we find moderate charge density fluctuations and observe deviations from linear dependence of dDNA on φc-1. This last result, together with other findings such as the decrease in the effective stretching modulus of the complex and the increased rate at which pores are formed in the complex membranes, are indicative of the gradual loss of mechanical stability of the complex, which occurs when φc becomes large. We suggest that this may be the origin of the recently observed enhanced transfection efficiency of lamellar CL-DNA complexes at high charge densities, because the completion of the transfection process requires the disassembly of the complex and the release of the DNA into the cytoplasm. Some of the structural properties of the system are also predicted by a continuum free energy minimization. The analysis, which semiquantitatively agrees with the computational results, shows that that mesoscale physical behavior of CL-DNA complexes is governed by interplay among electrostatic, elastic, and mixing free energies.