We have developed a "two-site" lattice gas model which provides a theoretical framework for understanding adsorption equilibrium in systems for which the potential energy surface is inherently heterogeneous in terms of both adsorbate-adsorbate and adsorbate-potential energy surface interactions and also entropic factors associated with the existence of two types of sites. Utilizing this general framework, we have examined two model systems with general features of the CO-Pt(111) adsorption system. In the first of these models, we represent the CO-CO interaction with a repulsive dipole-dipole - dipole-image potential and in the second, with a Lennard-Jones 6-12 potential. We delineate criteria for determining the ordered ground states of each of the systems in terms of the relative magnitudes of adsorbate-adsorbate and adsorbate-potential energy surface interactions and, utilizing Monte Carlo simulations, we calculate approximate phase diagrams for each. In addition to observing the expected order-disorder phase transitions, we observe a "bridge-to-top" transition associated with the transfer of molecules from bridge to energetically favored top sites as the temperature of the system is decreased. Both models produce phase diagrams which may be inferred from LEED studies of the CO-Pt(111) system at low coverages. In addition, the dipole-dipole - dipole-image potential reproduces quantitatively the experimentally observed coverage dependence of both the heat of adsorption and the infrared frequency of linear CO, while the Lennard-Jones model fails to reproduce these trends. We have utilized our model to address several issues related to the equilibrium of the CO-Pt(111) system and we suggest avenues for future experimental study.