Integrated energy system (IES) integrates various energy subsystems such as electricity, natural gas, heat, and the dynamic characteristics of different energy networks differ significantly. To realize the coordinated operation of heterogeneous energy flow network of electricity, natural gas, and heat, in this paper, a multi-spatial-temporal-scale coordinated optimal scheduling method of IES considering frequency support ability is presented. The method divides the IES into three layers on the spatial scale and divides IES optimal scheduling into three stages: day-ahead, intra-day and real-time on the temporal scale. In the day-ahead stage, the most economical day-ahead scheduling plan is developed. In the intra-day stage, considering the different response characteristics of the device, the slow, medium, and fast subsystem layers are divided for control, and the device output related to cold, heat, electricity, and natural gas is controlled hierarchically based on distributed model predictive control. In the real-time stage, the supporting effect of IES on power grid frequency is fully explored, and an IES active-frequency-support control method considering frequency regulation cost is proposed. Case studies show that the devices can be fully utilized with different response ability to perform the scheduling plans of each layer, effectively reducing the system operation cost and improving the frequency quality.