Lattice theories have been used extensively to predict and correlate liquid-liquid equilibria in mixtures. Lattice theories also have been used to predict the behavior of gases adsorbing onto solid surfaces. Here, we use a lattice model based on the ideas of Ono and Kondo to predict the phase behavior in adsorbed monolayers for systems that are below their bulk-phase critical points. For such an analysis, it is important that molecular behavior in the bulk and the adsorbed layer is based on consistent assumptions. Here, this is accomplished by treating the fluid in the bulk as well as in the adsorbed layer as a strictly regular solution. Interesting new adsorption isotherms and phase diagrams are generated that provide useful insights into adsorption of both lattice gases (i.e., "mixtures" of molecules and holes) and dense lattice liquids (i.e., "mixtures" of molecules without holes), illustrating the similarities between adsorption of gases and liquids.