Multi-layer films suitable as sealable or peelable sheet that can be used for closing foodstuff containers are described. These multi-layer films includes a polymeric substrate layer and a seal or a peel-seal layer. The multilayer composite film preferably includes four component layers, namely in order, a polymeric base layer for mechanical strength, a thin organic barrier layer, an ethylene polymer-based adhesive layer, and a heat seal layer including an ethylene copolymer, such as ethylene vinyl acetate copolymer. The film is useful as a peelable heat sealable lid for containers of diverse polymer compositions storing various products such as foodstuffs and pharmaceuticals.