Disclosed are coextruded multilayer film or sheet comprising at least four alternating layers of layer materials A and B, the layers having an average layer thickness of from 1 to 3000 nm, wherein layer material A comprises a cyclic olefin polymer, layer material B comprises an ethylene polymer and, based on layer materials A and B, one layer material is from 5 to 95 volume percent of the film or sheet and the other makes up the balance. In some of the embodiments the layers of A and B have a total thickness of at least 40 nm and the disclosed film or sheet can also comprise outer skin layers C and optional inner layers D which comprise from 5 to 95 volume percent of the film or sheet.