A battery housing having a battery chamber sealed to prevent the penetration of moisture and which accommodates at least one battery module, and a pressure equalization device to compensate for pressure fluctuations between the battery chamber and its outside environment. The pressure equalization device comprises a pressure equalization chamber fluidly connected to the battery chamber and a separating member arranged therein. The separating member is sealed off from the inner wall of the pressure equalization chamber, wherein the fluid connection with the battery chamber opens in a first chamber region of the pressure equalization chamber which is separated by the separating member from a second chamber region. The separating member permits a volume change in one of the chamber regions given a corresponding volume change in the other chamber region. The second chamber region is in fluid communication with the outside of the battery chamber via a venting path.