Although the energy hub (EH) concept results in different benefits, the system uncertainties might affect the optimized decisions. Several studies have studied EH’s optimal operation, considering the system uncertainties. However, there is a research gap in proposing a novel EH’s robust optimal operation under various charging modes of electric vehicles (EVs), besides integrated electrical and thermal demand response programs (DRPs). The main purpose of this research is to fill such a knowledge gap. In this paper, the uncertainties of renewable energy distributed resources and electricity price have been concerned using the robust optimization method. The integrated charging load of EVs under coordinated and uncoordinated charging modes has been distinguished using the Monte Carlo simulation (MCS). Another contribution is to study different schemes of hybrid electrical, heat, and cooling energy storage systems in the introduced robust framework. Simulation results infer that a 15.87% decrement in EH’s operation cost is achievable by applying the integrated thermal and electrical DRPs, using the electric heat pump (EHP) and hybrid storage system consisting of the ice storage system. The comparative test results show that the advantages of integrated thermal and electricity DRPs and charging management of EVs are highlighted by using EHPs. The sensitivity analyses of the EH’s operation cost against the robustness efficiency parameters corresponding to the uncertainty level show that the advantages of the proposed method are highlighted while the EH’s uncertainties increase.