A composite membrane comprises: a first layer of high-density polyethylene (HDPE) and a layer of asphalt applied over the first layer of HDPE. A second layer of HDPE sheeting is applied over the layer of asphalt. A method of creating a composite barrier to chemical vapors is also disclosed which comprises applying a base layer comprising high density polyethylene (HDPE); applying an asphalt layer over the base layer; and applying a top layer comprising HDPE over the asphalt layer.