The miscibility behavior of three binary mixtures, solvent with solvent, polymer with solvent, and polymer with polymer, was studied by use of a combination of the Flory-Huggins theory and molecular simulation techniques. Fundamental parameters in the Flory-Huggins theory, including the heat of mixing associated with pairwise interactions (Aw12) and the number of possible interaction partners, i.e., coordination number, z, are calculated from molecular simulations. The pair energies (~11, w22, ~12) are obtained by averaging a large number of confiations generated by a Monte Carlo approach which includes the constraints associated with excluded volume. The temperature dependence of the interaction parameter x is obtained with the formalism developed in this study. In all cases, the calculated upper critical solution temperatures compare favorably with experimental values. This approach provides an opportunity to test the Flory- Huggins theory for a number of model binary systems and to characterize their miscibility behavior. This combined approach also facilitates study of the thermodynamic behavior of a binary mixture without possessing specific knowledge or experimental data of the system under investigation.