With the development of distributed energy resources, peer-to-peer (P2P) electricity-hydrogen energy trading in multi-microgrids has obtannnnined great attention. However, the traditional trading model is over-simplified, especially, some important equipment affiliated to the electrolyzer has been overlooked. The potential of multi-energy trading model has not been fully utilized, resulting in no significant decrease in the operation cost of multi-energy microgrids. This paper presents a novel trading framework considering the purification subsystem to reduce the operating cost of multi-microgrids. The non-purified hydrogen can participate in energy trading based on purification sharing mechanism with multiple-material hydrogen pipes. To ensure the profit of each microgrid in trading market, we design the optimization for the energy trading using Nash bargaining theory. Considering the slow convergence in the traditional distributed algorithms, a novel self-adaptive mechanism for the convergence acceleration is provided. To validate the effectiveness of proposed framework, numerical cases are constructed based on three microgrids. The results demonstrate that the total operating cost of multi-microgrids can reduce by 5.50% through the proposed energy trading framework. Based on the self-adaptive mechanism, the number of iterations reduces by 50% and the convergence fluctuation is eliminated.