A package for maintaining a modified atmosphere around contents being contained therein when stored in an ambient environment is set forth. The modified-atmosphere package includes a tray, a membrane, and a structural member. The tray has a base and side walls extending upwardly from the base. The side walls and the base define a cavity wherein the contents are disposed. A membrane is attached to a top portion of the side walls and encloses the cavity. The structural member is detachably connected to the top portion of the side walls and is disposed above the membrane to prevent the membrane from contacting an external structure which inhibits permeation through the membrane. The structural member also has at least one opening for exposing the membrane to the ambient environment. Stacking means at the base of the tray and the top of the structural member allow the modified-atmosphere packages to be easily stacked. A vented-environment package is also shown which is very similar to the modified-atmosphere package except the permeable membrane is absent and the tray has at least one opening at its base. This opening on the lid is at least partially aligned with the base opening on the tray and simultaneously exposed to the ambient environment when two vented-environment packages are stacked. The lids utilized on the vented-environment package and the modified-atmosphere package are interchangeable.