The authors propose a hierarchical Marshall-Olkin model of countrywide systemic risk. At the lower level, the authors model the systemic risk of a crisis within the banking system (that we call “within” systemic risk) and at the higher level the authrs model the probability of a joint default of the banking system and the public sector (that we call “between” systemic risk). As for the within systemic risk, the authors propose a technique, that they call Cuadras-Augé filter, to extract the probability intensity of a systemic event. The authors apply the model to Europe and they find that, during the financial crisis, the within systemic component of the default risk in the banking sector has significantly increased in all countries, with the exception of Germany and the Netherlands. As for the between systemic risk, the authors find that Italy, Germany and Ireland share the same correlation between the time to default of the financial and public sectors (around 70%). However, for Italy all the between systemic risk is with the financial sector, while all the idiosyncratic risk is with the public sector: a systemic crisis affecting the banking sector is always associated with the default of the public sector, while the public sector could default for sector-specific reasons not related to banks. The authors' interpretation is that in Italy it is the weakness of public finances which hurts banks, and not vice-versa. For other countries, like Germany and Ireland, the opposite holds: a default of the public sector would necessarily be associated with a systemic default crisis of the financial sector, while a crisis in the financial sector could develop even in absence of a sovereign default. The reason is that the weakness and the size of banks have put a heavy burden on the governments of those countries, while the transmission channel of credit risk in the opposite direction is much less relevant.