The response potential of demand-side resources is becoming increasingly significant in integrated energy system (IES) operations. In addition, to ensure the effective participation of system devices, their actual responsiveness at different timescales should be considered. Based on these considerations, this paper proposes an IES multi-timescale operation optimization strategy that incorporates multiple forms of integrated demand response (IDR) and considers the response characteristics of the equipment. First, the multi-timescale characteristics of IDR are analyzed. Moreover, a multi-timescale operation model of IES that comprises day-ahead, intraday, and real-time stages is further established. In the day-ahead dispatch, a low-carbon economic scheduling model is developed by considering the shifting demand response (DR) and the cost of carbon emissions. In the intraday scheduling, noting that cooling and heat energy transmission possess slow dynamic characteristics, a rolling optimization model for cooling/heating coupled equipment considering load shedding and substituting DR is established. In real-time scheduling, the output of electric/gas coupled equipment is adjusted. Finally, an industrial park-type IES in northern China was selected as an example for a case study. The results show that (1) the IDR multi-timescale response strategy can exploit different types of demand-side flexibility resources. After implementing the shifting DR, the peak-to-valley difference of the electric load curve was reduced by 20%, and the total system cost was reduced by 2.3%. After implementing load shedding, the maximum load differences per unit period of the electric, heat, and cooling load curves decreased by 18.7%, 40.0%, and 68.9%, respectively. (2) By refining the timescale of IES optimization, the proposed model can effectively ensure the energy supply and demand balance of the system under different load scenarios and reduce the system operation cost. After applying the model to simulation in three typical days (transition season, summer, and winter), the penalty costs of lost loads reduce by ¥3650, ¥3807, and ¥3599, respectively, and the total system costs decrease by 17.4%, 16.1%, and 16.2%, respectively.