Comprehensive energy systems can synergize multiple forms of energy to meet user-side load demand, making full use of renewable energy for energy supply. However, the system often suffers from high instability in renewable energy supply or high variability in demand during operation, resulting in a mismatch between system supply and demand. This mismatch directly affects the energy supply efficiency of the system. The traditional single optimization approach, e.g., the two-stage co-optimization approach, has limitations in achieving both economic and energy savings, particularly as it does not consider the time scale. To address these issues, this study proposes a design framework for a two-layer collaborative optimization approach that incorporates multiple time scales and demand response coordination. The upper layer optimizes the capacity of the energy storage system, while the lower layer optimizes the coordinated operation of the energy supply facilities. In the lower layer optimization, the day-ahead scheduling phase considers tariff-based demand response to shift and curtail hot and cold electricity loads. The intraday optimization stage adjusts the results of the day-ahead scheduling to further optimize energy distribution and utilization, enhancing system economics and environmental friendliness. Analyzed in conjunction with practical cases, the results demonstrate that the optimization method improves the operational stability of the system and can reduce the total annual operating cost by 7.61%. Increasing the use of hybrid energy storage in the integrated energy system reduces total annual operating costs by 4.01%. If the use of demand response is added to the integrated energy system, the total annual operating cost can be reduced by 5.38%. This paper provides a theoretical reference for integrated energy system operation optimization studies.