We study and predict the interfacial tension, solubility parameters, and Flory-Huggins parameters of binary mixtures as functions of pressure and temperature, using multiscale numerical simulation. A mesoscopic approach is proposed for simulating the pressure dependence of the interfacial tension for binary mixtures, at different temperatures, using classical dissipative particle dynamics (DPD). The thermodynamic properties of real systems are reproduced via the parametrization of the repulsive interaction parameters as functions of pressure and temperature via molecular dynamics simulations. Using this methodology, we calculate and analyze the cohesive energy density and the solubility parameters of different species obtaining excellent agreement with reported experimental behavior. The pressure- and temperature-dependent Flory-Huggins and repulsive DPD interaction parameters for binary mixtures are also obtained and validated against experimental data. This multiscale methodology offers the benefit of being applicable for any species and under difficult or nonfeasible experimental conditions, at a relatively low computational cost.