A composite backer board for wet space construction is disclosed, along with a method of producing the backer board. The board includes a rigid foam core of a suitable thickness for wet space construction. A first fabric layer is fixed to at least one face of the rigid foam core with a polymeric adhesive. A first polymer layer is on the first fabric layer in which the polymer layer is dimensionally stable parallel to the face of the rigid foam core. A second fabric layer is on the first polymer layer opposite the first fabric layer and forms a first face that is amenable to thin set mortar and related compositions in wet space construction.