We follow the effect of osmotic pressure on isoelectric complexes that self-assemble from mixtures of DNA and mixed neutral and cationic lipids. Using small angle x-ray diffraction and freeze-fracture cryo-electron microscopy, we find that lamellar complexes known to form in aqueous solutions can reversibly transition to hexagonal mesophases under high enough osmotic stress exerted by adding a neutral polymer. Using molecular spacings derived from x-ray diffraction, we estimate the reversible osmotic pressure-volume (Π-V) work needed to induce this transition. We find that the transition free energy is comparable to the work required to elastically bend lipid layers around DNA. Consistent with this, the required work is significantly lowered by an addition of hexanol, which is known to soften lipid bilayers. Our findings not only help to resolve the free-energy contributions associated with lipid-DNA complex formation, but they also demonstrate the importance that osmotic stress can have to the macromolecular phase geometry in realistic biological environments.