Packages for moisture containing products, such as cheese, including a polyamide layer, an ethylene vinyl alcohol (EVOH) layer, a sealant layer, and a moisture barrier layer located between the sealant layer and the polyamide and EVOH layers. The moisture barrier layer may contain a blend of high density polyethylene (HDPE) and low density polyethylene (LDPE). The package film has a thickness of less than 3.5 mils and a moisture vapor transmission rate (MVTR) at 100.degree. F. and 90% relative humidity of less than 0.59 g/100 in.sup.2 per 24 hours. The moisture barrier layer minimizes the absorption of moisture by the polyamide layer, and thus prevents the package from forming a mottled appearance.