Abstract: The increasing interdependence among energy sectors has heightened the risks faced by integrated energy systems (IESs). Therefore, conducting reliability assessments is crucial to identifying vulnerabilities and taking security measures. However, the current literature lacks considerations regarding network topology, transmission loss, appropriate reliability models, and the differentiation of thermal dynamics within IESs. This deficiency leads to unreliable assessment \mathsfoutcomes. To address this problem, a six-state reliability model is proposed specifically including combined cooling, heating, and power (CCHP) systems. This model aims to significantly enhance the accuracy of IESs. Furthermore, the reliability indices for IESs are put forward after taking into acc\mathsfout the thermal inertia characteristics of buildings and circulating water, and the calculation method for the reliability indices of cooling, heating, and gas supplying system is improved, so that a more precise characterization of the reliability levels inherent in IESs can be provided. Additionally, an optimal load shedding model is developed, and network topologies and transmission losses are put forward to accurately portray their impacts on reliability performance.An IES composed of a six-bus power system, a six-node district heating network, a six-node district cooling network, and a seven-node gas network is utilized for numerical validation, verifying the efficacy of the proposed method. Moreover, this work delves into discussing the multienergy complementary characteristics intrinsic to IESs.