A structure for building applications, and method of making the same is provided. The structure can include a substrate layer having a first surface and a second, opposing surface and a cross-linked coat layer deposited on at least a portion of the first surface of the substrate layer. The cross-linked coat layer can include a mixture of polyvinyl alcohol and polycarboxylic acid. The multilayer structure can be configured to promote egress of water vapor in a first direction from the cross-linked coat layer to the substrate layer when the relative humidity is greater adjacent the cross-linked coat layer than adjacent the substrate layer and configured to inhibit ingress of water vapor in a second direction from the substrate layer to the cross-linked coat layer when the relative humidity is greater adjacent the substrate layer than adjacent the cross-linked coat layer.