This paper studies how banks’ balance sheets and funding costs interact in the transmission of monetary-policy rates to banks’ credit supply to firms. To do so, we use credit-registry data from Germany and Portugal together with the European Central Bank’s policy-rate cuts in mid-2014. The pass-through of the rate cuts to banks’ funding costs differs across the euro-area currency union because deposit rates vary in their distance to the zero lower bound (ZLB). When the distance is shorter, banks’ financing constraints matter less for the supply of credit and there is more risk taking. To rationalize these findings, we provide a simple model of an augmented bank balance-sheet channel where in addition to costly external financing, there is screening of borrowers and a ZLB on retail deposit rates. An impaired pass-through of monetary policy to banks’ funding costs reduces their ability to lever up and weakens their lending standards.