We develop a multivariate credit risk model for the term structures of sovereign and bank credit default swaps. First, we separate the probability of joint defaults of large Eurozone sovereigns (systemic risk) from that of sovereign-specific defaults (country risk). Then, we quantify individual banks' exposures to each type of sovereign risk, as well as bank-specific credit risk. Banks’ sovereign risk exposures vary with banks’ size, their holdings of sovereign debt, and expected government support. On average, 45% of French and Spanish banks' credit risk consists in sovereign risk, compared with only 30% for Italian and 23% for German banks. Furthermore, short- to mediumterm contracts are particularly informative on sovereign systemic risk.