As a rule, the polymeric membranes have low permeability in separation of low molecular weight components. In spite of this fact, the membrane processes have significant advantages compare with conventional technologies, in particular, low energy consumption and environmental friendliness. To improve transport properties of the polymer membrane their modification should be carried out. In the present work, the development of highly methanol-permeable pervaporation membranes based on poly-m-phenylene isophthalamide (PA) is achieved by two strategies: (i) modification of PA by novel synthesized and characterized highly stable metal–organic framework UiO-66(NH₂)-EDTA particles and (ii) development of supported membranes with thin selective layer on the regenerated cellulose substrate. First time the composite structure has been simulated: atomistic molecular dynamics simulations demonstrate the partial penetration of polymer inside the modifier and confirms the nature of the interaction between polymer and modifier assessed by spectroscopic methods. The optimal characteristics in respect of industrial use are obtained for supported PA/UiO-66(NH₂)-EDTA (15%) membrane: 1.55 kg/(m²h) permeation flux and 93.1 wt% methanol in the permeate for the separation of azeotropic methanol/toluene mixture.