Bidirectional wireless communication between two nodes is enabled by a half-duplex relay node using a two-phase decode-and-forward protocol. In the first phase, the messages of two nodes are transmitted to the relay node, which broadcasts a superposition of the re-encoded messages in the succeeding, phase. Individual mean transmit power constraints averaged over both phases are considered so that they are inversely proportional to the time division between the phase. An equivalent characterization of the achievable rate region with optimal time division is presented. Moreover, it is proved that the rate region is convex, which makes efficient algorithmic optimization solutions feasible.