Many energy systems rely on natural gas to fulfil their energy demand. In particular, natural gas is often used in the heating sectors as well as for electrical generation. In such systems, a comprehensive analysis of the system's resilience must account for the interdependencies between the electricity, heat, and gas sectors. Furthermore, the development of different gas supply sources can impact their ability to meet the peak day's demand. For example, liquefied natural gas (LNG) regasification facilities have a dependence on LNG delivery dates, which impact on the quantity of gas stored on a given day. In this paper, an integrated electricity-heat-gas network model has been developed for a holistic evaluation of the resilience of an energy system. Case studies based on Great Britain evaluate the impacts of gas supply shocks and LNG delivery timetables on the systems' resilience during time of extreme (cold) weather and low electricity outputs from renewable generation. The results highlight the need for gas network flexibility through reverse-flow compressors and diversity of supply sources.