One of the main barriers for the wide penetration of fuel cell electric vehicles is the lack of proper infrastructures for hydrogen transportation that hinders the implantation of refuelling stations. This barrier could be overcome by deploying onsite hydrogen generators based on mature electrolysis and hydrogen storage technologies. This way, the necessity of hydrogen transportation is avoided. In addition, electrolysers can be onsite supplied by means of renewable generators like photovoltaic panels, while the produced hydrogen can also be destined to generate electricity through fuel cells thus obtaining a monetary revenue. Thereby, the economy of the system may be improved in order to make viable this kind of infrastructures. However, the optimal coordination of the different assets is challenging and requires the use of energy management tools to pursue the optimal performance of the installation. In this kind of infrastructures, the energy management problem is performed under substantial uncertainties; moreover, these unknown parameters have a very different character. Thus, while energy pricing and renewable generation can be forecasted using conventional techniques, refuelling demand is highly unpredictable. To this end, this paper proposes a novel stochastic-interval model for the optimal scheduling of photovoltaic-assisted refuelling stations. The new proposal uses interval notation to model the inherent uncertainty of renewable generation and energy pricing, while the vehicle demand is modelled using a more suitable approach based on scenarios. In this regard, a comprehensive stochastic model for fuel cell electric vehicles is developed, which is based on reported driving behaviour and common characteristics of commercial vehicles. To solve the problem subjected to uncertainties, an iterative solution methodology is developed which allows adopting risk-seeker and risk-averse operational strategies. A case study is analysed to validate the new proposal and discussing the importance of the different economic activities that can be exploited in refuelling stations. Results reveal the importance of selling energy to the grid in order to complement the revenues obtained from refuelling; however, this process is highly impacted by uncertainties and the operational strategy, observing variations up to 50% in the total profit depending on the strategy adopted.