This paper addressed the optimal operation of the microgrids (MGs) containing both the electrical and thermal loads. Combined Heat and Power (CHP) units, boilers, wind turbines, storage devices, Demand Response Resources (DRRs), as well as the power exchange possibility with the upstream wholesale market are the energy resources that have been considered as the portfolio of the decision maker. The aim of the MG operator is to provide the electrical and thermal loads of the network in the most economic and flexible way. Therefore, suitable metrics are developed in this paper in order to evaluate the flexibility of the system for both the electrical and thermal units. Then, considering both the flexibility and financial concerns, a multiobjective framework is proposed. The Information Gap Decision Theory (IGDT) method is employed to handle the uncertainties of the proposed problem. Since the objectives of the MG operator might be conflicting with each other, an efficient optimization approach should be employed to properly satisfy the operator’s policies. The Normalized Normal Constraint (NNC) approach is employed here as an efficient method that is able to find the evenly distributed Pareto solutions. The IEEE 33-bus test system is utilized to simulate the proposed problem and analyze the results. The performance of the proposed problem is approved using different scenarios. The simulation results justify the advantages and necessities of the proposed problem.