Composite membranes include a polymer material that is selectively permeable to heavy (C3+) hydrocarbons over methane. The polymer material may be a modified poly(dimethylsilane) having a backbone including dimethylsiloxyl monomers, substituted methylsiloxyl monomers, and internal-network monomers. The substituted methylsiloxyl monomers may include phenylmethylsiloxyl monomers or C5-C10 alkylmethylsiloxyl monomers such as octylmethylsiloxyl monomers. The polymer material may include silicon-alkyl linkages such as Si—(CH2)n—Si, where n≥2 that may create a structure that imparts desirable permeability and selectivity characteristics to the composite membrane. The polymer material may be cast onto a porous support material. The composite membranes may be incorporated into systems or methods for removing heavy hydrocarbons from natural gas.