Using a new monthly dataset on bank-level lending rates, we study the transmission of conventional and unconventional monetary policy in the euro area via shifts in the supply of credit. We find that a bank lending channel is operational for both types of measures, though its functioning differs: for standard operations the transmission is weaker for banks with more capital and a more solid funding structure, in line with an important role of asymmetric information. However, in response to non-standard measures lending supply expands by more at banks with stronger capital and funding positions, suggesting a crucial role for regulatory and economic constraints. We also find that the transmission of unconventional measures is attenuated by their negative effect on future bank's capital position via the net interest income (reverse bank capital channel). Finally, we find that large sovereign exposures mute the response of lending rates to conventional policy, but amplify the transmission of unconventional measures.