We consider two-way interference channels (ICs) where there are forward and backward ICs, but not
necessarily the same. We consider a scenario where two independent forward messages and the backward IC is exploited only for the purpose of feedback for aiding forward-message transmission. For a ADT deterministic IC, we derive a new outer bound which matches with a developed inner bound for certain range of channel parameters. As a consequence, the sum capacity is fully characterized for all channel parameters.