A household appliance has a housing and a door that define an interior, and an electric controller. A measuring device is disposed in the interior for measuring a physical parameter and includes a measuring probe and a probe antenna. A lighting device for illuminating the interior of the household appliance includes a cover and a transmit or receive antenna. The transmit or receive antenna is disposed on the housing and sealed from the interior in a substantially airtight manner using the cover. The transmit or receive antenna is in signal communication with the electric controller allowing wireless signal transmission between the measuring probe and the electric controller.