A coextruded multilayer film includes a core layer including an ethylene vinyl alcohol copolymer; two intermediate layers each including a blend of an amorphous polyamide having a glass transition temperature of at least 80° C., and a semicrystalline polyamide; two outer layers each including an olefinic polymer; and two tie layers each adhering an intermediate layer to a respective outer layer; wherein the film exhibits an elongation at yield (ASTM D 882) of less than 15% in each of the longitudinal and transverse directions, and a free shrink (ASTM D 2732) at 200° F. of less than 8% in each of the longitudinal and transverse directions. An aseptic package includes a sterilized food product, and a sterilized pouch in which the sterilized food product is disposed, the sterilized pouch including the coextruded multilayer film of the invention. A method of making an aseptic package is also disclosed.