•A modified third-order quantized state system (MQSS3) simulation method is proposed.•An event-driven framework is developed for the co-simulation of EH-IES using MQSS3.•Better performance is achieved in simulations of EH-IES with continuous-discrete properties.•Detailed dynamics can be derived to support the precise operation analysis of EH-IES. Effective simulation methods are becoming critically essential for the analysis of integrated energy systems (IESs) to reveal the interactions of multiple energy carriers. The incorporation of various energy technologies and numerous controllers make the IES a heterogeneous system, which poses new challenges to simulation methods. This paper focuses on the simulation of an IES with hybrid continuous-discrete properties and heterogeneous characteristics. First, a modified third-order quantized state system (MQSS3) method is proposed for the simulation of district heating systems (DHSs), in which quantized state system (QSS) and time-discretized integration are integrated to efficiently manage numerous discrete control actions. Second, an event-driven framework is established to integrate MQSS3 into the simulation of the electricity-heat integrated energy system (EH-IES). This framework enables the adoption of the most suitable models and algorithms for different systems to accommodate the heterogeneous properties of an IES. Case studies of an EH-IES with maximum 80% PV penetration and 210 buildings demonstrate that the dynamic interactions between the DHS and the power distribution network are accurately illustrated by the proposed simulation methods, in which MQSS3 indicates the highest simulation efficiency. It is also demonstrated in the simulation results that the flexibility from DHS can be utilized as demand-side resource to support the operation of power distribution network in aspects such as consuming the surplus PV generations.