This paper proposes a day-ahead optimization framework for the sustainable energy supply of an electric vehicle (EV) charging park and hydrogen refueling station (HRS) outfitted with the power-to‑hydrogen (P2H) conversion facility in a local multi-energy system (LMES). A novel integrated demand response (IDR) program with an incentive mechanism is used for power and heat demands, EV charging park, and HRS to further improve system flexibility and operational costs. A hybrid multi-objective information-gap decision theory/robust optimization (HMIRO) framework is also applied as an effective modeling technique for dealing with existing uncertainties with no need for a probability density function and scenario creation. The suggested HMIRO model is formulated as a tri-level mixed-integer linear programming (MILP) problem and converted into a single-level MILP problem using duality theory that enables the LMES operator to utilize two risk-averse strategies simultaneously due to the information-gap on uncertain parameters. The numerical results indicate that the proposed hybrid risk-averse strategy enables the LMES operator to guarantee a risk reduction of wind generation and HRS demand up to 20.6 % and 14.3 %, respectively, in day-ahead optimization while leading to a 5 % increase in the daily operation cost. Also, the daily energy cost can be reduced by up to 3.52 %, 2.88 %, 7.03 %, and 1.15 % with optimal IDR implementation for power load, heat load, EV charging park, and HRS in LMES, respectively.