We infer a term structure of interbank risk from spreads between rates on interest rate swaps indexed to the London Interbank Offered Rate (LIBOR) and overnight indexed swaps. We develop a tractable model of interbank risk to decompose the term structure into default and non-default (liquidity) components. From August 2007 to January 2011, the fraction of total interbank risk due to default risk, on average, increases with maturity. At short maturities, the non-default component is important in the first half of the sample period and is correlated with measures of funding and market liquidity. The model also provides a framework for pricing, hedging, and risk management of interest rate swaps in the presence of significant basis risk.