We study the diversity-multiplexing tradeoff (DMT) for the slow fading interference channel with a relay (ICR). We first derive an outer bound on the DMT based on the cut-set bound. We then derive two inner bounds on the DMT: One is based on the compress-and-forward relaying scheme and the other is based on the decode-and-forward relaying scheme. We find conditions on the channel parameters and the multiplexing gains under which the proposed inner bounds achieve the optimal DMT. We also identify cases in which the DMT of the ICR is the same as two parallel fading relay channels, implying that interference does not decrease the DMT for each pair, and that a single relay can be DMT-optimal for two pairs simultaneously. Lastly, we identify conditions under which adding a relay strictly improves the DMT relative to the interference channel without a relay.