The form of hybrid AC/DC is a trend in power distribution systems. The resilience against extreme weather depends on the coordination of cyber and physical systems. Therefore, it is necessary to study the post-disaster recovery of AC/DC hybrid cyber-physical distribution systems (CPDSs). Voltage source converters (VSCs) are critical cyber-physical devices in hybrid AC/DC distribution systems (HDSs) that offer flexibility in post-disaster recovery. However, existing literature on the role of VSC commonly ignores the unreliable communication. In this paper, we quantify the impact of communication failures on VSCs and propose an adaptive switching model of VSC control modes that enhances both the emergency islanding and service restoration phases of post-disaster recovery. This paper also introduces a scheduling model of multi-type repair resources including power failure repair crews, communication failure repair crews, and emergency communication vehicles for joint the restoration of CPDSs. The system recovery model is also presented. Finally, a novel optimization framework combining adaptive switching of VSC control modes, scheduling of multi-type repair resources, and system recovery is proposed to improve the post-disaster recovery efficiency. The effectiveness and superiority of the proposed framework are demonstrated through numerical experiments in a modified IEEE 123-bus system.