A heat-sealable polymer-based multilayer film for peelably and releasably packaging pasty or fatty foods comprising a polymer-based core layer having a food-facing side and an exterior-facing side, a peelable layer on the food-facing side of the core layer, the peelable layer having a food-facing side and a core-facing side, and the peelable layer containing a peeling agent, and an interior skin layer on the food-facing side of the peelable layer, the interior skin layer having a food-facing side and a core-facing side. The core layer contains a release agent for diffusion toward the interior skin layer, and the release agent is present in the core layer in a quantity which is greater than the saturation capacity of peeling agent in the peelable layer for the release agent.