This article proposes a planning model for a multi-energy microgrid (MEM) that supplies the electricity, heating, and cooling loads. This controls flexible demands and provides continuous control in the presence of smart and comprehensive programming of electricity, heat, ice, compressed air, and hydrogen energy storage. The features of the MEM are considering the losses and amortization costs of electricity, heating and cooling energy storage, and the operating area of the combined heat and power (CHP) units in the planning procedure. Besides, the principle of convexity in the CHP unit operation area is attended. The proposed formulation is applicable in days of summer and winter seasons for a variety of planning studies. The outcomes represent that utilizing the proposed MEM planning results in significant advantages for the power network and the consumer. The cost savings are respectively obtained equal to 33% and 34% in the winter and summer seasons. The cost savings can be considered besides the investiture cost of MEM elements to specifying the MEM profits made during the designing step. Another valuable result is the cost-saving of PHEV smart charge about 1.38 times of PHEV smart discharge for summer and about 1.05 for winter. It also makes the curve of demand optimal utilization from the demand response program and energy storage plan.