When several combined cooling, heating and power (CCHP) microgrids are connected to an active distribution network, the microgrid and network serve as different stakeholders, and the economic optimal dispatch of the system becomes more complex. To protect privacy, an economic optimal dispatch model of an active distribution network with CCHP microgrids is proposed. Chance-constrained programming is used to deal with the randomness of new energy and cooling, heating and power load in the CCHP microgrids. The distributed modeling method is adopted to minimize the operating cost of each region. Analytical target cascading (ATC) is used to determine the optimal economic dispatch results in their respective regions in parallel. At the same time, the introduction of an integrated demand response (IDR) in the user side of the CCHP microgrid is conducive to reducing energy supply costs. Verification on an improved IEEE33-bus system example shows that the introduction of IDR can effectively reduce the operating cost of the system. The optimal economic dispatch results of the active distribution network and CCHP microgrids can be obtained using ATC and protect the privacy of each region. This work is supported by the National Natural Science Foundation of China (No. 61963026).