The aim of this paper is to show how qualified investors in cat bonds can offer adequate pandemic business interruption protection in a comprehensive public–private coverage scheme. First, we propose a numerical model to expose how cat bonds can contribute to complement standard re/insurance by improving coverage of cedents even though risks are positively correlated during a pandemic. Second, we introduce double trigger pandemic business interruption cat bonds, which we name PBI bonds, and discuss their precise characteristics to provide efficient coverage. A first trigger should be pulled when the World Health Organization declares a Public Health Emergency of International Concern (PHEIC). The second trigger determines the payout of the bond based on the modelised business interruption losses of an industry in a country. We discuss moral hazard, basis risk, correlation and liquidity issues which are critical in the context of a pandemic. Third, we simulate the life of theoretical PBI bonds in the restaurant industry in France by using data gathered during the COVID-19 pandemic.