As the interdependencies of power systems and gas networks escalate, further coordinated efforts are required to effectively deal with resiliency issues caused by weather-related incidents. This paper proposes a flexible operation planning framework to improve the resiliency of integrated power and gas distribution systems (IPGDSs) during weather-related events. In this framework, the problem is formulated as a two-stage optimization model. The first stage is associated with temporary network hardening problem, in which the crews of power distribution system and gas network cooperatively harden critical components by considering the constraints of the operator’s situational awareness, human sources, hardening budget, and transportation congestion. The second stage determines operational resiliency-improvement measures, e.g., switching scheme for dynamic multi-microgrid formation, scheduling of distributed generators and storage devices (electrical and gas), and shedding plan for power and gas loads. To extract high-potential scenarios during severe weather-related events, this framework incorporates the spatial and temporal features of the events, and the generation uncertainties of renewable energy sources, by using Monte Carlo simulation. The column-and-constraint generation (C&CG) approach is adopted to solve the problem. The effectiveness of the proposed framework is validated through case studies performed on IEEE 33-Bus and a real-world 492-Bus systems, integrated with an actual 30-Node gas network.