In this paper we model the term structures of sovereign and bank credit default swaps by using a multivariate credit risk model. First, the probability of joint defaults of large Eurozone sovereigns (systemic risk) is separated from that of sovereign-specific defaults (country risk). Then, individual banks' exposures to each type of sovereign risk, as well as bank-specific credit risk, are quantified. Banks' exposures to each type of sovereign risk vary with their size, holdings of sovereign debt, and expected government support. On average, 45% of French and Spanish banks', but only 30% of Italian and 23% of German banks' credit risk is sovereign risk. Furthermore, short- to medium-term contracts are particularly informative on sovereign systemic risk.