Certain lipid monolayers at the air-water interface undergo a second-order transition from a tilted to an untilted liquid-crystalline state of their lipid hydrocarbon chains at sufficiently large lateral pressure. Recent experimental observations demonstrate that in the presence of divalent cations DNA adsorbs onto a zwitterionic lipid monolayer and decreases the tilt transition pressure. Lowering of the tilt transition pressure indicates that the DNA condenses the lipid monolayer laterally. To rationalize this finding we analyze a theoretical model that combines a phenomenological Landau approach with an extension of the Poisson-Boltzmann model to zwitterionic lipids. Based on numerical calculations of the mean-field electrostatic free energy of a zwitterionic lipid monolayer-DNA complex in the presence of divalent cations, we analyze the thermodynamic equilibrium of DNA adsorption. We find that adsorbed DNA induces a 10% reduction of the electrostatic contribution to the lateral pressure exerted by the monolayer. This result implies a small but notable decrease in the tilt transition pressure. Additional mechanisms due to ion-ion correlations and headgroup reorientations are likely to further enhance this decrease.