The wireless multiple-unicast problem is considered over a layered network, where the rates of transmission are limited by the relaying and interference effect. The deterministic model is used to capture the broadcasting and multiple access effects. The capacity region of the Z-chain relay-interference network is fully characterized. In order to solve the problem, we introduce a new achievability scheme based on ``interference neutralization'' and a new analysis technique to bound the number of non-interfering (pure) signals.