Assembly intended to be arranged in an aircraft cockpit having a pressurized cabin, in order to supply a breathing gas to a crew member, said assembly comprising a respiratory mask having an oronasal face cover and a harness, the oronasal face cover having a respiratory cavity and being suitable for applying on the face of the crew member around the mouth and nose, the harness forming a loop adapted to be extended around the head of the user on a side opposite from the oronasal face cover so as to hold the oronasal face cover on the face of the user, and a storage device, said storage device comprising a base and a platform, the platform being mounted so as to be movable relative to the base between a retracted position and an extended position, the platform having a receiving surface, the receiving surface of the platform being adapted to receive the respiratory mask in a storage position where the harness holds the oronasal face cover against the receiving surface of the platform by encircling the platform to form a loop extending around the platform on the opposite side from the oronasal face cover, the respiratory mask being releasable from the storage device.