The invention provides a composite structure containing a foam layer, an inner layer and an outer layer of a thermoplastic compact cover layer, and a lacquer layer in this order, and having a tensile strength according to DIN EN ISO 527-3 at 2000 mm/min and 23° C. of less than 5 MPa in both a first direction and a second direction perpendicular to the first direction, wherein the density of the foam layer is 40 to 150 kg/m3, the inner layer contains particles of an elastomer (polymer (F)) and at least 50 wt % of a thermoplastic polyolefin (polymer (E)) and is directly bonded to the outer layer, the outer layer differs from the inner layer in its composition and contains the following polymers (A) to (C) in a total amount of 100 parts by weight: 25 to 70 parts by weight of particles of an elastomer (polymer (A)), 0 to 40 parts by weight of a low-density polyethylene (polymer (B)), and 20 to 70 parts by weight of a thermoplastic polyolefin (polymer (C)) other than polymer (B). The invention provides the use of the composite structure in car interiors, in particular as airbag cover, a method for the production of the composite structure.