A barrier assembly. The barrier assembly includes at least one barrier stack having at least one barrier layer and at least one polymer layer. The barrier stack has an oxygen transmission rate of less than 0.005 cc/m.sup.2/day at 23.degree. C. and 0% relative humidity, and an oxygen transmission rate of less than 0.005 cc/m.sup.2/day at 38.degree. C. and 90% relative humidity. The barrier stack also has a water vapor transmission rate of less than 0.005 g/m.sup.2/day at 38.degree. C. and 100% relative humidity. A method for making a barrier assembly is also disclosed.