Tunneling using the drilling and blasting method induces a blasting damaged zone around the tunnel, which affects the tunnel stability as well as the resulting support design. In this article, an analytical model that represents the whole-process interaction between the sequentially installed composite linings and the surrounding rock in the presence of the blasting damaged zone is proposed. First, assuming the blasting damaged zone to be a finite cylinder with decreased mechanical parameters, four ground forms according to the distribution of plastic zone are categorized and solved. Furthermore, the fictitious pressure concept is adopted to represent the three-dimensional effect of tunnel advancement, and thus, the construction process of the tunnel can be simulated. After that, the evolution patterns of the whole-process interaction between the composite linings and ground are distinguished. The critical distances and tunnel displacements between different forms in various interaction stages are identified and solved. Finally, the analytical solutions for tunnel displacement and structural responses can be obtained, based on the displacement compatibility conditions between composite linings and the ground. The analytical model is validated by numerical simulations through several typical examples, and the applicability in actual tunnel support design is verified by field monitoring results. Comparisons with an existing model and the conventional convergence-confinement method illustrate the inherent nature and advantages of the proposed model in the support system design. It is found that the blasting damage effect is significant on the tunnel responses, which should be considered in the support design. The proposed model provides a convenient feasible approach in determining the stiffness and support time of the composite linings for tunnels using the drilling and blasting method.