The integration of microgrids and the combined cooling heating and power (CCHP) systems can foster a better utilization of energy. In order to achieve economic optimization and peak-load reduction of the CCHP microgrids model, this paper proposes a multi-objective optimal scheduling model for CCHP microgrids integrated with renewable energy, energy storage system and incentive based demand response. First, linearization methods are applied to change the original nonlinear optimization model into a mixed-integer linear programming (MILP) problem. Then, an augmented ε-constraint (AUGMECON) method is implemented to solve the multi-objective optimization problem (MOP). Finally, the final scheme is selected from the obtained Pareto optimal set by fuzzy clustering method according to the preference of decision maker. The results show that the CCHP microgrids is effective in reducing pollutant gas emissions and reducing the cost of treating them. And compared with the other four intelligent algorithms, the proposed MILP method has better accuracy and computational efficiency. In addition, with the inclusion of the peak-load shifting function, the interruptible load and the battery can effectively respond to peak load changes by shifting the peak of the exchange power curve in the point of common coupling (PCC) of the CCHP microgrids. In the end, the sensitivity analysis is carried out and the results present that electricity price, natural gas price, and the efficiency of PV have varying degrees of impact on model performance.