To combat energy shortage, the multi-energy system has gained increasing interest in contemporary society. In order to fully utilize adjustable multi-energy resources on the demand side and reduce interactive compensation, this paper presents an integrated demand response (IDR) model in consideration of conventional load-shedding and novel resource-shifting, due to the fact that participants in IDR can use more abundant resources to reduce the consumption of energy. In the proposed IDR, cooling, heating, electricity, gas and so forth are considered, which takes the connection between compensation and load reductions into consideration. Furthermore, a bilevel optimal dispatch strategy is proposed to decrease the difficulty in coordinated control and interaction between lower-level factories and upper-level multi-energy operators in industrial parks. In this strategy, resources in both multi-energy operator and user sides are optimally controlled and scheduled to maximize the benefits under peak shifting constraint. In the normal operation mode, this strategy can maximize the benefits to users and multi-energy operators. Particularly in heavy load conditions, compared to the conventional electricity demand response, there are more types of adjustable resources, more flexibility, and lower interactive compensations in IDR. The results indicate that optimal operation for factories and multi-energy operators can be achieved under peak shifting constraint and the overall peak power value in industrial park is reduced.