With the development of energy intelligent technology, integrated energy system (IES) has been widely used in the field of energy supply. While the IES significantly improves energy efficiency, the interaction between different energy systems may also bring multiple operational risks to the reliability of the energy supply, which necessitates an effective IES reliability assessment technique. Considering the dynamic characteristics of gas and heat systems can reduce energy losses during contingencies, which provides an instrument to improve the IES reliability. This paper for the first time contributes to a novel emergency dispatch formulation based on the IES dynamic optimal energy flow (OEF). A reliability assessment framework for IES is proposed by combining the IES dynamic OEF and Monte Carlo simulation (MCS). By taking into account the emergency dispatch formulation, the unreliability degree of IES can be mitigated. The IES dynamic OEF model is transformed into a linear programming problem under reasonable assumptions and simplifications due to its high degree of nonlinearity. Several novel reliability indices for heat system are proposed by incorporating the impacts of the IES dynamic characteristics on the reliabilities. The proposed model and method are validated by using an integrated gas, power and heat testing system