Multilayered barrier structures containing a gas barrier layer of a non-chlorine containing organic polymer which is substantially impermeable to oxygen gas and a moisture barrier layer of a mesophase propylene-based material are provided. These structures are environmentally compatible and radiation resistant, and exhibit one or more additional properties, including gas barrier properties, moisture barrier properties, toughness, heat sealability, softness, and quietness during wrinkling. Also provided are methods of preparing and using such multilayered barrier structures, and articles, such as films, pouches, and tubings, formed from these structures.