Thin-film membranes based on polyphenylene oxide composites with a varying concentration of heteroarm star-shaped polymers (1, 3, and 5 wt %) comprising arms of polystyrene and poly(2-vinylpyridine)- block-poly(tert-butylmethacrylate) diblock copolymer grafted onto a common fullerene C-60 core have been developed. The transport properties of the membranes have been studied in the pervaporation separation of a methanol-ethylene glycol mixture. An increase in the star-shaped polymer content in the membrane leads to an increase in the flux and separation factor of the membranes. Sorption studies have revealed that the sorption activity of methanol in the membranes is higher than that of ethylene glycol. The introduction of star-shaped polymer additives into the membrane composition leads to an increase in the degree of equilibrium sorption of the two components of the mixture subjected to separation. The formation of transport channels in pervaporation membranes during sorption in deuterated methanol has been first studied using the small-angle neutron scattering method. Comparative analysis of the data on neutron scattering on the original dry samples, the samples saturated with deuterated methanol, and the samples dried after sorption has shown that the structural uniformity of the composite membranes is higher than that of the matrix polymer. According to scanning electron microscopy, the morphology of the composite membranes is a system of closed cells.