Climate risks often do not happen in isolation but can compound with other sources of stress such as pandemics and pre-existing financial vulnerabilities, particularly in emerging countries. Compounding events increase the complexity of risk, leading to cascading impacts in the economy and finance. Thus, tailoring macroeconomic models to include compound risk considerations can inform effective recovery policies, avoiding to underestimate risk. We build on the EIRIN macrofinancial model (Monasterolo & Raberto, 2018, 2019) to quantitatively assess the direct and indirect impacts of compound COVID-19 and climate physical risks in the economy and finance, accounting for the fiscal and monetary policy response to shocks. EIRIN captures the richness of climate risk transmission to the economy and finance in a rigorous accounting framework. In addition, EIRIN explicitly embeds a financial sector and financial market, thereby allowing the analysis of the impact of financial feedbacks on endogenous investment and consumption decisions, and on policy effectiveness. Then, via a compound risk indicator, we quantify the non-linearity of compound risk on GDP through time. We calibrate the model on Mexico, a country that is highly exposed to hurricane hazard and COVID-19, and deeply integrated in the global value chain, representing a potential channel of cascading risks. We show that compounding climate physical and COVID-19 risk can give rise to non-linear dynamics that amplify losses, with implications on private and public debt sustainability. The initial shocks’ magnitude and their specific risk transmission channels contribute to explain the evolution of compound risks, given the country’s pre-shock characteristics. Credit market constraints can amplify the shock by limiting firms’ recovery investments, thus mining the effectiveness of increasing fiscal spending. Fiscal policies that depart from a business as usual recovery, and align to climate objectives, could help to build resilience to compound risk, avoiding increases in countries’ divergence and debt sustainability challenges.