A composite material contains a nonwoven layer (i) which contains fibers formed from a first thermoplastic elastomer having meshes with a mesh size in the range from 10 to 100 μm, and a membrane layer (ii) which contains a second thermoplastic elastomer and having a layer thickness of less than 30 μm. The membrane is either pore-free (ii.1) or is porous and has pores with an average pore diameter of less than 2000 nm (ii.2). The membrane (ii) is at least partially in direct contact with the fibers of the nonwoven layer (i) and covers the mesh openings in the nonwoven layer (i) at least partially. The fibers of the first nonwoven layer (i) and the membrane (ii) in the contact area are at least partly joined to one another in an interlocking manner.