Technologies are generally described for composite membranes which may include a porous graphene layer in contact with a porous support substrate. In various examples, a surface of the porous support substrate may include at least one of: a thermo-formed polymer characterized by a glass transition temperature, a woven fibrous membrane, and/or a nonwoven fibrous membrane. Examples of the composite membranes permit the use of highly porous woven or nonwoven fibrous support membranes instead of intermediate porous membrane supports. In several examples, the composite membranes may include porous graphene layers directly laminated onto the fibrous membranes via the thermo-formed polymers. The described composite membranes may be useful for separations, for example, of gases, liquids and solutions.