Battery housing with protective cover, battery and motor vehicle

The invention relates to a battery housing (1) for a battery of a motor vehicle, which is designed to accommodate at least one battery cell of the battery, and which has:-at least one membrane-like venting element (6), which is arranged on a housing wall (2) of the battery housing (1) and is designed to vent the at least one membrane-like venting element (6) into the housing wall (2) of the battery housing (1); the at least one battery cell yields when the hot gas of the at least one battery cell exits into the interior (3) of the battery housing (1) and in this case releases an exhaust opening (4) in the housing wall (2) for discharging the hot gas from the interior (3) into the surroundings (5) of the battery housing (1); and-at least one protective cover (7) which is arranged on the outer side of the housing wall (2) so as to overlap the at least one venting element (6) in order to protect the at least one venting element (6) from the surroundings and which is fastened to the housing wall (2) by means of a