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Power-to-gas (P2G) is a promising solution to the issue of non-dispatchable renewable power generation. However, the high investment costs and low energy efficiency of P2G systems pose challenges. This study designs a green hydrogen-based Energy Storage as a Service (ESaaS) mode to improve the economic efficiency of P2G systems. In this ESaaS mode, the P2G system acts as an energy trading hub. The ESaaS operator manages the system and enables microgrids to access energy storage services. In return, the ESaaS operator generates revenue through electricity and hydrogen trading. To characterize stakeholders' behaviors, we develop a cost-minimizing model for multi-energy microgrid operation and a revenue-maximizing model for P2G investment and operation. To coordinate stakeholders involved in cooperation, we employ Nash bargaining-based model reformulation to determine investment and operation decisions and benefit distribution. Then, logarithm transformation and trading price discretization are introduced to efficiently solve the non-convex and nonlinear reformulated model. Simulation experiments using Shanghai's electricity market and meteorological data demonstrate that the ESaaS mode achieves 100% recovery of surplus renewable electricity and increases the proportion of renewable energy in microgrids from 59% to 83%. The results suggest that green hydrogen-based ESaaS is a feasible solution to increase the utilization rate of renewable energy and bring considerable economic and environmental benefits to all stakeholders.