In integrated energy system (IES), rapidly developmental integrated demand response (IDR) increases the demand-side flexibility. It is challenging to aggregate decentralized IDR resources to participate in multiple markets simultaneously with coordinating the profits of all market-driven stakeholders. To this end, this paper proposes a novel tri-layer decision-making framework for IES to investigate the interaction of IDR and multi-energy market clearing while coordinate complexly interactive stakeholders. In the first layer, electricity-gas wholesale market is cleared based on the offers and bids submitted by energy producers and integrated energy distribution system operator (IEDSO). In the second layer, IEDSO serves as a mediator between multi-energy market and integrated load aggregators (ILAs). Profit-maximizing IEDSO affects the market equilibrium prices by incorporating IDR resources to trade strategically in wholesale market, and offers flexible price strategies considering the changes in clearing results to exploit ILAs’ IDR potential. In the third layer, cooperative game theory is introduced to make ILAs can flexibly cooperate with each other or participate in IDR according to price signals, and Shapley value is used to avoid the conflicts of interest. Meanwhile, multiple uncertainties are dealt with by scenario method to mitigate their influence on multi-energy market operation. To solve this problem efficiently, a tailored reformulation and convexification scheme is developed to convert it into an equivalent mixed integer linear programming problem. Finally, case studies verify the effectiveness and practicality of the proposed tri-layer framework.