In a double-hazard scenario consisting of a public health event and a natural disaster, the public spreads a particular category of compound rumor involving both of these public safety events, referred to as compound rumors involving pandemics and natural disasters. To prevent the spread of compound rumors involving pandemics and natural disasters, it is important to release and spread debunking information specifically targeting such compound rumors. Recently, the coupling effects of different disasters in terms of information dissemination have been confirmed. This study speculates that the spread of debunking information targeting compound rumors involving pandemics and natural disasters may similarly be influenced by such coupling effects, resulting in an amplification phenomenon to reach a broader audience, thereby aiding in alleviating the negative impacts of rumors. This study establishes a debunking information spread model applicable to double-hazard scenarios consisting of public health events and natural disasters, aiming to describe the spread process of debunking information in such contexts. Furthermore, this study conducts empirical research using a real double-hazard case consisting of the earthquake and the public health event that occurred in Sichuan, China, in 2022. It demonstrates the amplification phenomenon in the spread of debunking information targeting compound rumors involving pandemics and natural disasters. In addition, it validates the effectiveness of the new proposed model. This study provides guidance for rumor management, facilitating the more effective dissemination of debunking information to mitigate the harm caused by rumors.