The self-healing ability of distribution systems (DSs) against extreme events can be significantly boosted by strategically dispatching mobile emergency resources (MERs). In recent years, the penetration of hydrogen energy in energy systems has increased dramatically. Hydrogen energy and its related infrastructure, such as hydrogen refueling stations (HRSs) and mobile fuel cell vehicles (MFCVs), exhibit great potential for enhancing the self-healing ability of DSs. In this work, a two-layer hierarchical strategy for improving the restorative self-healing ability of hydrogen-penetrated DS (HPDS) with multiple microgrids (MGs) and HRSs is proposed considering their interactions and MERs such as mobile energy storages and MFCVs. In the lower layer, an optimal energy management strategy is presented for MGs considering the coordination between hydrogen and electricity via the electrolyzer and fuel cell in the HRSs. In the upper layer, an energy sharing (ES) strategy is proposed for the distribution system operator (DSO) to dispatch MERs in order to minimize the power imbalance among MGs and reduce the unserved load. Since MERs can be dispatched for many times to swap energy and hydrogen between MGs or HRSs, the concept of the equivalent time network (ETN) is introduced, and based on the ETN, a mixed integer linear programming (MILP) model is innovatively proposed to represent the traveling pattern of MERs and to optimize their ES path among MGs. Finally, the two-layer hierarchical strategy is formulated as MILP models and solved using the commercial solver. Case studies on a modified IEEE 33 bus distribution system (DS) and a regional DS in China verify the effectiveness of the proposed strategies.