This paper analyzes the way in which international financial integration affects the transmission of monetary policy in a New Keynesian open economy framework. It extends Woodford's (2010) analysis to a model with a richer financial markets structure, allowing for international trading in multiple assets and subject to financial intermediation costs. Two different forms of financial integration are considered, in particular an increase in the level of gross foreign asset holdings and a decrease in the costs of international asset trading. The simulations in the calibrated model show that none of the analyzed forms of financial integration undermine the effectiveness of monetary policy in influencing domestic output and inflation. Under realistic parameterizations, monetary policy is more, rather than less, effective as the positive impact of strengthened exchange rate and wealth channels more than offsets the negative impact of weakened interest rate channels. The paper also analyzes the interaction of financial integration with trade integration, varying both the importance of trade linkages and the degree of exchange rate pass-through. These interactions show that the positive effects of financial integration are amplified by trade integration. Overall, monetary policy is most effective in parameterizations with the highest degree of both financial and real integration.