Hydrogen - electricity coupled DC microgrids (HE-DCMGs) represent a promising and sustainable solution for off-grid power supply. However, achieving high economic performance while ensuring DC bus voltage stability is a critically challenging task. This study proposes a hierarchical energy management and control strategy for HE-DCMGs that integrates an adaptive mutation Harris hawks optimization (AMHHO) algorithm at the system level with a fractional-order sliding mode controller (FOSMC) at the device level. A multi-objective optimization problem is formulated to minimize hydrogen consumption and reduce degradation of proton exchange membrane fuel cells and lithium-ion batteries. The AMHHO algorithm, augmented with differential evolution and Lévy flight mechanism, determines the optimal power allocation among distributed sources, while the FOSMC provides robust DC bus voltage regulation. The proposed strategy is validated on a 750 V HE-DCMG experimental platform capable of 168 hours of off-grid operation. Experimental results show that the proposed strategy reduces long-term operating costs and improves energy-utilization efficiency, achieving an overall system efficiency of 80.49%-97.37%. The DC bus voltage is maintained with a response time of 0.02 s, a low overshoot of 3.7%, and a voltage fluctuation rate of 3.08%, all of which comply with the requirements of IEEE Std 1547‒2018.