There is provided breathable overpressure assemblies that are secured to a sealed container and configured to rupture in the event of a rapid pressure increase and to regulate pressure inside the container. A breathable overpressure assembly includes a rupture member having a central rupture portion and a peripheral flange extending about at least a portion of a periphery of the central rupture portion. The breathable overpressure assembly includes at least one vent opening in at least one of the central rupture portion and the peripheral flange, and a breathable membrane that covers the at least one vent opening.