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In this work we consider the achievable rates of a joint resource allocation for a three-node network where a half-duplex relay node enables bidirectional communication between nodes 1 and 2 and thereby adds an own multicast message to the communication. In the multiple access phase nodes 1 and 2 transmit their message to the relay node, which decodes the messages and forwards them in the succeeding broadcast phase. Therefore, the relay node encodes the multicast and bidirectional messages using the superposition encoding strategy. We do not allow cooperation between the encoders of nodes 1 and 2, but since both nodes know a priori its own bidirectional message, both nodes can cancel the interference caused by their own message before decoding the unknown messages. It shows that for both nodes it is always optimal to decode the relay message first. Furthermore, the total sum-rate maximum is determined by the sum-rate optimum of the bidirectional broadcast phase. From the closed form solutions of the combinatorial problems we can characterize the bidirectional rate pairs where the total sum-rate remains constant. In the end the obtained results are discussed and illustrated by means of some working examples. The joint resource allocation improves the overall spectral efficiency and enables new trade-offs between the routing tasks.