Integrated energy system (IES) is an effective solution for energy and environment problems. In view of the difficulty of traditional reliability assessment methods to reasonably and effectively assess the reliability of the IES, an energy supply reliability assessment method based on sequential Monte Carlo simulation is proposed in this study. The optimal operation of the system is realised by mobilising the multi-energy complementary characteristics during device failure. The reliability of the system under three different operation objectives is compared and analysed. Three new reliability indices are proposed, which take into account the supply of multiple energy loads and the differences among different energy. Finally, through the analysis of energy supply reliability under different objectives, the reasonability of the proposed indices and the flexible scheduling of energy flow under different objectives are verified; therefore, the IES can realise adaptive and targeted operation strategy during device failure. Also, the influence of different device faults on the system's energy supply reliability is ranked, which is of great significance to find the weak parts of the system and provide a reference for the system to improve energy supply reliability.