A composite structure contains a lofty corrugated nonwoven web of polymeric microfiber that is maintained in a corrugated condition by securing a fabric to the corrugated web at the valleys of the corrugations. The composite structure is made without substantially effecting web loft by (i) introducing the nonwoven web to the ends of a plurality of spaced paddles, (ii) causing the spacing between the ends of the paddles to decrease to corrugate the nonwoven web, and (iii) securing the fabric to the corrugated nonwoven web at the valleys of the corrugations. A composite structure of this construction made by this method provides very good filtration performance, making it particularly suitable for use as a filter in a cup-shaped face mask. The composite structure also is very suitable for use as thermal insulation in apparel.