A method is proposed for the synthesis of new membrane materials based on polydimethylsiloxane (PDMS) and polybutadiene (PB). It has been shown that all components of the mixture completely enter into the hydrosilylation reaction and form a chemically crosslinked composite material. It has been found that in the region of low PB concentrations, the composite has a less crosslinked and dense structure. The gas transport properties of the synthesized materials have been experimentally investigated. The proposed materials have higher selectivity for organic components than the industrially used membrane polymer PDMS, which is determined by their high sorption selectivity. A membrane containing 17 wt % PB has enhanced fluxes of organic components and an increased separation factor for all alcohols (ethanol, n-propanol, and n-butanol) examined relative to those of the PDMS membrane in the pervaporative separation of water-alcohol solutions. At the same time, the ethanol-water permselectivity of such a membrane is greater than 1, a value that has been first achieved by modifying PDMS with polymers. Materials of this type have a great potential for the creation of membranes with high permeability and selectivity in the recovery of volatile organic compounds from aqueous media.