The composite elastic material (22) includes an elastic layer (4) and a structured film layer (15) having first and second opposing surfaces, with the second surface bonded to the elastic layer (4). The first surface of the structured film layer (15) has upstanding male fastening elements. The structured film layer (15) is gathered such that the upstanding male fastening elements point in multiple directions. The composite elastic material (22) can also be called a stretch-bonded laminate, which include an elastic layer (4) stretch- bonded to a second surface of a structured film layer (15). A first surface of the structured film layer (15), opposite the second surface, has upstanding male fastening elements. A process for making the composite elastic material (22) is also described. An absorbent article including the composite elastic material (22) is also described.