In a full-duplex bidirectional interference network with $2K$ transceivers, there are $K$ communication pairs: each user transmits a message to and receives a message from one intended user and interferes with and experiences interference from all other users. All nodes may interact, or adapt inputs to past received signals, and may thus co-operate with each other. We derive a new outer bound, and use interference alignment to demonstrate that the optimal degrees of freedom (DoF, also known as the multiplexing gain) is $K$ : full-duplex operation doubles the DoF, but interaction and co-operation does not further increase the DoF. We next characterize the DoF of a full-duplex bidirectional interference network with a MIMO full-duplex relay. If the relay is noncausal/instantaneous (at time $k$ forwards a function of its received signals up to time $k$ ) and has $2K$ antennas, we demonstrate a one-shot scheme where the relay mitigates all interference to achieve the interference-free $2K$ DoF. In contrast, if the relay is causal (at time $k$ forwards a function of its received signals up to time $k-1$ ), we show that a full-duplex MIMO relay cannot increase the DoF of the full-duplex bidirectional interference network beyond $K$ , as if no relay or interaction is present.