A packaged food product includes a food product and a package enclosing the food product. The package may be formed from a coated, printed film that includes a substrate film including one or more thermoplastic materials and having an average thickness of less than about 15 mils. An image is printed on the print side of the substrate film. A radiation-cured varnish covers the printed image. The radiation-cured varnish was formed by coating the printed image with a radiation-curable varnish that includes one or more polymerizable reactants and optionally one or more photointiators. The radiation-curable varnish is subsequently exposed to radiation sufficient to polymerize at least 90 weight % of the polymerizable reactants. When the coated, printed film is tested according to the FDA migration test protocol, no more than 50 parts per billion total of any of the polymerizable reactants and the optional photoinitiators migrate within 10 days at 40.degree. C. from the coated, printed film into a food simulant of 95 weight % ethanol and 5 weight % water enclosed within a test container formed from the coated, printed film so that the food simulant contacts the food side of the substrate film and the ratio of volume of food simulant to surface area of coated, printed film is 10 milliliters per square inch.