This paper presents a multi‐objective restoration scheme for improving the resilience of integrated electricity and natural gas distribution systems against extreme weather events. The coupling constraints of electricity and gas networks are tackled properly using a linearized optimal power flow (OPF). Distributed generators, power‐to‐gas facility, rescheduling of generation/storage units, and microgrid formation are employed as operational resources/measures for restoring the integrated energy system after the event landfall. An adaptable directed multi‐commodity flow‐based microgrid formation is utilized, that is, the network configuration is dynamically changed in accordance with time‐variant load priority weights. The proposed method was successfully examined on an integrated electricity and natural gas distribution system comprised of the modified IEEE 33‐bus distribution network and a 14‐node natural gas distribution network. Numerical results showed that using microgrid formation increased the supplied critical load of integrated electricity and natural gas distribution system by about 16%. Moreover, due to making benefit of the power‐to‐gas unit, the supplied critical load increased by about 12.3%. respectively. While utilizing energy storage systems along with the power‐to‐gas unit facilitated the exchange of energy between the power distribution network and natural gas distribution network regarding time‐variant load priority weights, the supplied critical load increased by about 13%.