Under the retail electricity market reform and the development of demand-side integrated energy systems in China, the Integrated Energy Service Agency (IESA) is responsible for purchasing energy from the external market and supplying it to multi-energy users (MEUs). However, with the increase in the types of MEUs, the IESA has gained more sales options. How to meet the required MEU participation level in the integrated demand response (IDR) plan to ensure that the IESA sets the optimal integrated energy price is an urgent problem. In this paper, a bi-level optimal low-carbon economic dispatch model for an industrial park is proposed considering multi-energy price incentives; at the upper level, the model takes the optimal net income of the IESA as the target, and the carbon emission constraints of the real-time unit integrated energy supply are considered, so that the IESA can reasonably dispatch a comprehensive energy supply, optimize the operation of energy conversion equipment, and set reasonable energy selling prices based on energy prices in the external market. At the lower level, the model takes the minimum integrated energy cost to MEUs as the goal. MEUs take the initiative to obtain retail energy price signals, formulate optimal multi-energy use strategies, and actively participate in the IDR plan. At the same time, coordination between the upper and lower levels helps to optimize the price of the energy sold and the power used by the IDR and is therefore used to achieve the overall environmental and economic requirements of the industrial park. The prime dual path following the interior point method is used to solve the nonlinear, multidimensional, and double-iterative optimization model, and three typical examples are used to illustrate that the model and method can improve the net income of the IESA, ensure the economic and environmental protection of the cooperative multi-energy operation, and encourage MEUs to actively participate in the IDR plan.