Considering the limited information sharing between natural gas systems (NGS) and electrical power systems (EPS), this paper proposes a distributed resilience assessment method for NGS and EPS. First, a coordinated restoration framework is presented for incompletely integrated energy systems, and the collaborative benefit redistribution mechanism is proposed to motivate the participation of the cooperative restoration. Then fragility and recovery models for NGS and EPS components are developed, involving the impact of wind and rainfall during typhoons. An emergency load shedding model considering the conditional value at risk under typhoons is built, where the dynamic constraints of gas storage in NGS's pipelines is considered, and a linear approximation method is adopted to make the solution feasible. The modified alternating direction method of multipliers algorithm is used to solve the problem, and herein the self-adaptive penalty factor is leveraged to boost the efficiency. Based on the valley-shaped resilience model, the concept of skewness and kurtosis are introduced to give risk-adverse metrics more systematically to the impact of extreme events. The proposed model and algorithm are validated by case studies. Except for the performance exploration, the weakness and enhancement suggestions are also concluded from the case analysis.