A composite membrane for separations includes a fabric with a non-woven array of intermingled carbon nanotubes, and a dopant incorporated with the fabric to form a non-porous, permeable composite. The composite membrane may be used to separate a target gas from a liquid by mounting the composite membrane in a housing chamber, and conditioning a permeate side of the chamber to establish a driving force for the target gas across the non-porous, permeable composite membrane.