Pervaporation is the purification technology which utilizes the transport properties of polymer membranes and has several important properties: energy efficiency, environmental friendliness, and a high degree of purification. To improve the transport properties, polymer membranes are modified with special nanoparticles. In this work we study the translational mobility of methanol and toluene molecules inside a poly-m-phenylene isophthalamide membrane with and without the nanoparticle of UiO-66 (NH2) metal-organic framework (UiO-66 (NH2) MOF) using full atomistic molecular dynamics simulation with microsecond trajectories. It was found that methanol has a high translational mobility inside the polymer matrix. Moreover, this mobility is significantly increased by addition of UiO-66 (NH2) MOF. Toluene molecules are practically immobile inside the polymer matrix and tend to form clusters with each other. Due to the inclusion of a nanoparticle, toluene molecules “get stuck” inside UiO-66 (NH2) MOF and its surface. We believe that the obtained results will contribute to the purposeful development and study of polymer matrices for the pervaporation process.