How does heterogeneity in banks’ interest-rate risk exposure shape monetary policy transmission? We develop a quantitative macroeconomic model of heterogeneous banks to answer this question. We establish an irrelevance result: differences in interest-rate risk exposure between fixed- and variable-rate banking systems matter for transmission only when bank solvency concerns become relevant. Calibrating the model to the euro area, we show that idiosyncratic default risk pushes a substantial share of banks toward the solvency threshold, making heterogeneity quantitatively important. When policy rates rise, fixed-rate banks suffer net interest margin compression—funding costs increase while legacy loan income stays unchanged—eroding capital and triggering sharper deleveraging. The lending elasticity to monetary policy is one-third larger in fixed-rate economies. The effects extend to financial stability: tightening raises bank failure rates in fixed-rate systems while lowering them in variable-rate systems. The results provide a rationale for macroprudential and monetary policy coordination and for monetary policy gradualism.