The fast development of technologies in the smart grids provides new opportunities such as co-optimization of multi-energy systems. One of the new concepts that can utilize multiple energy sources is a hybrid fuel station (HFS). For instance, an HFS can benefit from energy hubs, renewable energies, and natural gas sources to supply electric vehicles along with natural gas vehicles. However, the optimal operation of an HFS deals with uncertainties from different sources that do not have similar natures. Some may lack in term of historical data, and some may have very random and unpredictable behavior. In this study, we present a stochastic mathematical framework to address both types of these uncertainties according to the innate nature of each uncertain variable, namely: epistemic uncertainty variables (EUVs) and aleatory uncertainty variables (AUVs). Also, the imprecise probability approach is introduced for EUVs utilizing the copula theory in the process, and a scenario-based approach combining Monte Carlo simulation with Latin Hypercube sampling is applied for AUVs. The proposed framework is employed to address the daily operation of a novel HFS, leading to a two-stage mixed-integer linear programming problem. The proposed approach and its applicability are verified using various numerical simulations.