Hydrogen-based multi-energy systems (HMES) have emerged as a promising low-carbon and energy-efficient solution, as it can enable the coordinated operation of electricity, heating and cooling supply and demand to enhance operational flexibility, improve overall energy efficiency, and increase the share of renewable integration. However, the optimal operation of HMES remains challenging due to the nonlinear and multi-physics coupled dynamics of hydrogen energy storage systems (HESS) (consisting of electrolyters, fuel cells and hydrogen tanks) as well as the presence of multiple uncertainties from supply and demand. To address these challenges, this paper develops a comprehensive operational model for HMES that fully captures the nonlinear dynamics and multi-physics process of HESS. Moreover, we propose an enhanced deep reinforcement learning (DRL) framework by integrating the emerging representation learning techniques, enabling substantially accelerated and improved policy optimization for spatially and temporally coupled complex networked systems, which is not provided by conventional DRL. Experimental studies based on real-world datasets show that the comprehensive model is crucial to ensure the safe and reliable of HESS. In addition, the proposed SR-DRL approaches demonstrate superior convergence rate and performance over conventional DRL counterparts in terms of reducing the operation cost of HMES and handling the system operating constraints. Finally, we provide some insights into the role of representation learning in DRL, speculating that it can reorganize the original state space into a well-structured and cluster-aware geometric representation, thereby smoothing and facilitating the learning process of DRL.