In this work, we study the MIMO Gaussian bidirectional broadcast channel (BBC) with common message and characterize the capacity region. Moreover, we show that the transmit covariance matrix optimization problem has the same structure as the corresponding optimization problem of the BBC without common message which leads to the comfortable position to transfer results from one scenario to the other. This problem is motivated by the concept of bidirectional relaying in a three-node network, where a half-duplex relay node establishes a bidirectional communication between two other nodes and thereby adds an own multicast message to the communication.