Disclosed is a composition that comprises or is produced from a first ethylene α-olefin copolymer, a modified first ethylene α-olefin copolymer, and a second ethylene α-olefin copolymer or propylene α-olefin copolymer. Also disclosed is a multilayer film or sheet structure containing at least one barrier layer; at least one predominantly propylene-based layer, at least one predominantly ethylene-based layer, or both; and at least one adhesive layer produced from the composition. Further disclosed is a produced for producing a multilayer structure using the composition as adhesive layer.