With the extensive application of information and communication technology in distribution networks, the degree of cyber-physical coupling of distribution networks is gradually deepened. The existing reliability model of the cyber-physical system (CPS) of distribution networks is difficult to accurately evaluate the reliability of complex scenarios in practical engineering application. In this paper, multi-state reliability models are established for coupling components based on their failure cases, and cyber failure scenarios of the distribution networks are traversed based on the full binary tree topology. Thus, a novel reliability analysis method is proposed. This method takes into account the actual fault handling process and transfer capacity constraints, and it is applicable for all distribution networks with open-loop topologies. It provides a feasible method for evaluating the reliability of the stock CPS of distribution network. Finally, taking an actual distribution network in a city as an example, the feasibility and effectiveness of the proposed reliability evaluation method of the CPS of distribution networks is verified.