A fabric or belt for a papermaking machine including a first layer that defines a web contacting surface and a second layer that supports the first layer. The first layer is made of extruded polymer and includes a plurality of first elements aligned in a first direction, a plurality of second elements aligned in a second direction and extending over the plurality of first elements, and a plurality of open portions defined by the plurality of first and second elements. The second layer is made of woven fabric. The first layer is bonded to the second layer so that the first layer extends only partially through the second layer and an interface formed between. the first and second layers includes bonded and unbonded portions and airflow channels that extend in a plane parallel to the first and second layers.