Monetary policy has heterogeneous effects across euro area countries. There are strong correlations between cross-country monetary policy potency and housing and mortgage market institutions, namely the share of adjustable-rate mortgages and the homeownership rate. To disentangle the relative importance of these institutions, I incorporate them into a quantitative currency-union New Keynesian model with rich household balance sheets. I calibrate the model to Spain and the euro area. The model fits well: the consumption response in Spain is 2.4 times stronger than the euro area in the model relative to 2.5 in the data. My results reveal that a higher adjustable-rate mortgage share and a higher homeownership rate interact to amplify the effects of monetary policy on economic activity due to smaller mortgage interest payments and a higher fraction of mortgaged homeowners operating in the market. I use the model to show that a banking union requiring shared financial regulation decreases the heterogeneous effects of monetary policy by weakening the pass-through to average mortgage interest rates. Finally, including house prices into the euro area price index stabilizes output at the cost of less stable goods inflation.