In a double-hazard scenario consisting of a public health event and a natural disaster, a special type of compound rumor simultaneously involving of these two such different public safety events—epidemic-related natural disaster rumor— will be generated and spread. To prevent the spread of epidemic-related natural disaster rumor, it is important to release and spread the debunking information focusing on this such special type of rumors. Recently, the coupling interaction between different disasters at the information level in multi-hazard scenarios has been verified. This study considers that the spread of the debunking information of epidemic-related natural disaster rumor will amplify owing to this such coupling interaction, which helps more people get the debunking information to alleviate the negative impact brought from rumors. A debunking information spread model which is appropriate for the double-hazard scenarios consisting of public health events and natural disasters is established, and it is used to describe the spread process of debunking information. Furthermore, the real double-hazard case consisting of the earthquake and the public health event occurring in Sichuan, China, in 2022 has also been used to make an empirical analysis. It confirms the amplification of the debunking information of epidemic-related natural disaster rumor spreading and validates the effectiveness of the new proposed model as well. This study provides guidance and assistance for rumor management, helping the debunking information spread better to alleviate the harm of rumors.