There is little room for doubt that distributed generation systems including renewable energy, microgrids (MGs), combined heat and power (CHP) units and storage systems have been of particular importance in sustaining low-carbon and cost-effective operations due to the tremendous increase in greenhouse gas emissions in recent years. Additionally, hydrogen-based power technologies have earned a great deal of publicity that hydrogen can serve as a zero-emission fuel for electrical power and thermal energy production. In this regard, the current paper proposes an optimal energy management strategy for a combined hydrogen, heat, and power MG (CHHP-MG) with hydrogen fueling stations (HFSs) for hydrogen vehicles (HVs), electric vehicle parking lots (EVPLs) for electric vehicles (EVs) and fuel cell micro-CHP (FC-MCHP) units to meet power and heat requirements. In order to reduce the regular operating expense, the presented CHHP-MG could also communicate with both electricity and hydrogen markets. In addition, to compensate for the associated heat and hydrogen requirements, power-to-X technologies such as the power to heat (P2HT) and power to hydrogen (P2H) are integrated. In order to improve flexibility and build a low carbon MG, multi-energy storage (MES) system along with heat and power demand response (HPDR) programs will be taken into consideration. As the uncertainties associated with the predicted wind and photovoltaic power have a major impact on the energy management of the CHHP-MG, a multi-objective information gap decision theory (IGDT)-based robust approach is applied as an effective non-probabilistic modeling technique for handling such uncertainties. The empirical results show that the proposed model can efficiently handle the uncertainties and reduce the overall operation cost by 76.35%.