A multilayer film has a first layer and a second layer. The first layer comprises an additive, a binder, and a crosslinking agent. The additive is a flavor, fragrance, colorant, antimicrobial agent, antioxidant, chelating agent, and/or odor absorbent. The binder is a polysaccharide and/or a protein. The crosslinking agent comprises a compound with at least two carbonyl groups. The second layer comprises a non-water-soluble thermoplastic polymer comprising at least one member selected from the group consisting of polyolefin, polyamide, polyester, polyvinylidene chloride, polyvinyl chloride, and polystyrene. Each of the additive, binder, and crosslinking agent are present throughout a thickness of the first layer. Preferably, the first layer is coated onto the second layer, which is preferably a non-water-soluble thermoplastic polymer, e.g., polyolefin, polyamide, and/or polyester. The film is especially useful for cook-in applications, in which a food product (preferably comprising uncooked meat) is packaged in the film with the coated layer against the meat. The meat is then cooked and the additive transfers to the meat, and purge can be very low. The invention also pertains to a process for preparing a cooked food product, process for making a coated film, and articles formed from the film, such as bags and casings.