This paper uses a two-country, sticky-price model with non-atomistic wage setters to study the role of collective wage bargaining in the propagation of monetary shocks. I find that the welfare transmissions of a monetary expansion are reinforced by different labor market structures. Non-atomistic domestic unions anticipate that their wage demands raise real labor income through a movement of the terms of trade. This leads to an additional channel of transmission of monetary policy that goes through aggregate supply. Yet, workers benefit more from a monetary expansion when the exchange rate pass-through is not limited and the elasticity of substitution across traded goods is sizable. It follows that wage mark-ups charged by unions endogenously vary with those structural parameters. In particular, labor and product market distortions are strategic substitute in affecting the perceived labor demand elasticity.