A method of fabricating a composite membrane, includes the steps of: forming a first solution comprising a charged polymer and a first uncharged polymer having a repeat unit of a formula of: where each of X and Y is a non-hydroxyl group; forming a second solution comprising a second uncharged polymer; electrospinning, separately and simultaneously, the first solution and the second solution to form a dual fiber mat; and processing the dual fiber mat to form the composite membrane.