We study the functioning and possible breakdown of the interbank market in the presence of counterparty risk. We allow banks to have private information about the risk of their assets. We show how banks’ asset risk affects funding liquidity in the interbank market. Several interbank market regimes can arise: i) normal state with low interest rates; ii) turmoil state with adverse selection and elevated rates; and iii) market breakdown with liquidity hoarding. We provide an explanation for observed developments in the interbank market before and during the 2007-09 financial crisis (dramatic increases of unsecured rates and excess reserves banks hold, as well as the inability of massive liquidity injections by central banks to restore interbank activity). We use the model to discuss various policy responses.