Network models adeptly capture heterogeneities in individual interactions, making them well-suited for describing a wide range of real-world and virtual connections, including information diffusion, behavioural tendencies, and disease dynamic fluctuations. However, there is a notable methodological gap in existing studies examining the interplay between physical and virtual interactions and the impact of information dissemination and behavioural responses on disease propagation. We constructed a three-layer (information, cognition, and epidemic) network model to investigate the adoption of protective behaviours, such as wearing masks or practising social distancing, influenced by the diffusion and correction of misinformation. We examined five key events influencing the rate of information spread: (i) rumour transmission, (ii) information suppression, (iii) renewed interest in spreading misinformation, (iv) correction of misinformation, and (v) relapse to a stifler state after correction. We found that adopting information-based protection behaviours is more effective in mitigating disease spread than protection adoption induced by neighbourhood interactions. Specifically, our results show that warning and educating individuals to counter misinformation within the information network is a more effective strategy for curbing disease spread than suspending gossip spreaders from the network. Our study has practical implications for developing strategies to mitigate the impact of misinformation and enhance protective behavioural responses during disease outbreaks.