Epidemic transmission and the associated awareness diffusion are fundamentally interactive. There has been a burgeoning interest in exploring the coupled epidemic-awareness dynamic. However, current research predominantly focuses on self-protection behavior stimulated by awareness, paying less attention to self-isolation behavior. Given the constraints of government-mandated quarantine measures, spontaneous self-isolation actions assume greater significance in the long-term response to epidemics. In response, we propose a coupled awareness-epidemic spreading model with the consideration of self-isolation behavior and subsequently employ a Microscopic Markov Chain Approach to analyze the model. Extensive experiments show that self-isolation behavior can effectively raise the epidemic threshold and reduce the final outbreak scale. Notably, in multiplex networks with positive inter-layer correlation, the inhibitory effect is the greatest. Moreover, there exists a metacritical point, only when the awareness diffusion probability exceeds the critical value of this point, the epidemic threshold will increase with the increase of awareness diffusion probability. In addition, the growth of the average degree of the virtual-contact layer can reduce the value of this metacritical point. This research emphasizes the significant role of self-isolation behavior in curbing epidemic transmission, providing valuable perspectives for epidemic prevention through the interplay of awareness and epidemic spreading.