The emergence of epidemics has seriously threatened the running of human society, such as COVID-19. During the epidemics, some external factors usually have a non-negligible impact on the epidemic transmission. Therefore, we not only consider the interaction between epidemic-related information and infectious diseases, but also the influence of policy interventions on epidemic propagation in this work. We establish a novel model that includes two dynamic processes to explore the co-evolutionary spread of epidemic-related information and infectious diseases under policy intervention, one of which depicts information diffusion about infectious diseases and the other denotes the epidemic transmission. A weighted network is introduced into the epidemic spreading to characterize the impact of policy interventions on social distance between individuals. The dynamic equations are established to describe the proposed model according to the micro-Markov chain (MMC) method. The derived analytical expressions of the epidemic threshold indicate that the network topology, epidemic-related information diffusion and policy intervention all have a direct impact on the epidemic threshold. We use numerical simulation experiments to verify the dynamic equations and epidemic threshold, and further discuss the co-evolution dynamics of the proposed model. Our results show that strengthening epidemic-related information diffusion and policy intervention can significantly inhibit the outbreak and spread of infectious diseases. The current work can provide some valuable references for public health departments to formulate the epidemic prevention and control measures.