An airbag enclosure has a cover formed by a rigid panel having a portion forming a flap defined by a plurality of sides all formed as breakaway lines and one of which also forms a hinge. The cover is made of a thermoplastic laminate that has a plurality of first layers alternating with a plurality of second layers. The first layers each consist of a homogenous thermoplastic film of a polyolefin copolymer, polyester, or a polyester copolymer. The second layers each consist of an array of strips, fibers, or filaments of polypropylene or polyester.