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 and show that 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 euro-area-wide mortgage market 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.