We use a two-country New Keynesian model with balance sheet constraints to investigate the magnitude of international spillovers of U.S. monetary policy. Home borrowers obtain funds from domestic households in domestic currency, as well as from residents of the foreign economy (the United States) in dollars. We assume agency frictions are more severe for foreign debt than for domestic deposits. As a consequence, a deterioration in domestic borrowers' balance sheets induces a rise in the home currency's premium and an exchange rate depreciation. We use the model to investigate how international monetary spillovers are affected by the degree of currency mismatches in balance sheets, and whether the latter make it desirable for domestic policy to target the nominal exchange rate. We find that the magnitude of spillovers is significantly enhanced by the degree of currency mismatches. Our findings also suggest that using monetary policy to stabilize the exchange rate is not necessarily more desirable with greater balance sheet mismatches and may actually exacerbate short-run exchange rate volatility.