The phase equilibria associated with the binary Cu-Mg system are analyzed by applying results from first-principles calculations to a general solution thermodynamics treatment. Differing from previously reported models, we employ a four-species association model for the liquid, while the terminal and intermediate solid phases are modeled as substitutional solutions with one or two sublattices, respectively. The zero-Kelvin enthalpies of formation for the intermediate compounds, Cu2Mg-C15 (cF24) and CuMg2-Cb (oF48) are computed using the Vienna Ab-initio Simulation Package (VASP). The Gibbs free energy functions for the individual phases are evaluated, and the resulting binary phase diagram is presented over the full composition range. While the phase diagram we propose exhibits only modest deviation from previously reported models of phase equilibria, our treatment provides better agreement with experimental reports of heat capacity and enthalpy of mixing, indicating a more self-consistent thermodynamic description of this binary system.