In a three-node network bidirectional communication between two nodes can be enabled by a half-duplex relay node with a decode-and-forward protocol. In the first phase, the messages of two nodes are transmitted to the relay node. In the second phase a re-encoded, composition is broadcasted by the relay node. In this work the capacity region of the broadcast phase in terms of the maximal probability of error is determined. It is characterized by the mutual informations of the separate channels coupled by the common input.