Combined heat and power (CHP) microgrids (MGs) are a set of CHP units, boilers, power-only distributed generation (DG) units and storage systems that simultaneously supply heat and power demand. In this research, the objective is to provide a comprehensive mixed integer linear programming (MILP) model for unit commitment (UC) in CHP MGs including fossil-fueled power-only DGs, boilers, CHP units, photovoltaic, wind and geothermal power units, solar heater, battery charging station (BCS), adjustable thermal loads, battery energy storage (BES) and thermal energy storage (TES) units. In the proposed model, all operational constraints of CHP units, boilers and power-only units such as minimum up/down time and start-up/ shut-down ramp rate limits are considered and the commitment history of generation units prior to operation horizon is considered. In the proposed model, type II CHPs with non-convex feasible operating region (FOR) are used and their non-convex FOR is transformed into two convex FORs. The proposed model is solved with CPLEX solver in general algebraic modeling system (GAMS) which guarantees the achievement of the global optimum. The model is solved for different scenarios wherein the effect of BCS, effect of storage systems as well as the effect of adjustability of loads on MG operation is investigated. According to the results, BES and TES respectively decrease MG operation cost by 7.4% and 1.82%.and BCS adds 20.19% to the MG operation cost. The results also show that with replacement of adjustable thermal loads with evenly distributed loads, MG operation cost increases by 0.6%.