Credit default swaps (CDS) on a reference entity may be traded in multiple currencies, in that, protection upon default may be offered either in the currency where the entity resides, or in a more liquid and global foreign currency. In this situation, currency fluctuations clearly introduce a source of risk on CDS spreads. For emerging markets, but in some cases even in well-developed markets, the risk of dramatic foreign exchange (FX)-rate devaluation in conjunction with default events is relevant. We address this issue by proposing and implementing a model that considers the risk of foreign currency devaluation that is synchronous with default of the reference entity. As a fundamental case, we consider the sovereign CDSs on Italy, quoted both in EUR and USD. Preliminary results indicate that perceived risks of devaluation can induce a significant basis across domestic and foreign CDS quotes. For the Republic of Italy, a USD CDS spread quote of 440 bps can translate into an EUR quote of 350bps in the middle of the Euro-debt crisis in the first week of May 2012. More recently, from June 2013, the basis spreads between the EUR quotes and the USD quotes are in the range around 40bps. We explain in detail the sources for such discrepancies. Our modeling approach is based on the reduced form framework for credit risk, where the default time is modeled in a Cox process setting with explicit diffusion dynamics for default intensity/hazard rate and exponential jump to default. For the FX part, we include an explicit default-driven jump in the FX dynamics. As our results show, such a mechanism provides a further and more effective way to model credit/FX dependency than the instantaneous correlation that can be imposed among the driving Brownian motions of default intensity and FX rates, as it is not possible to explain the observed basis spreads during the Euro-debt crisis by using the latter mechanism alone.