Developing hydrogen-based multi-microgrid systems (HBMMSs) is vital to the low-carbon energy transition, which can promote the utilization of renewable energy and reduce carbon emissions. However, there have been no studies presenting a sustainability evaluation of HBMSSs. Multi-attribute decision-making (MADM) methods are widely used to perform a sustainability evaluation. This paper develops a triangular intuitionistic fuzzy framework to make a comprehensive evaluation of HBMMSs from the perspective of sustainability. Firstly, a sustainability evaluation criteria system including economic, social, environmental, technical, and coordination criteria is established. Secondly, the paper proposes a hybrid fuzzy decision-making method. A triangular intuitionistic fuzzy decision-making trial and evaluation laboratory technique is used to analyze the correlation between criteria and sub-criteria and provides a basis for determining their fuzzy densities. A ranking method combining the triangular intuitionistic fuzzy number, fuzzy measure, and Choquet integral is used to rank the alternatives and choose an optimal one. Moreover, a case study is performed to validate the practicability of the developed framework. Finally, sensitivity analysis, scenario analysis, and comparative analysis are conducted to verify the robustness and effectiveness of the framework. As such, this study provides a guide for evaluating the sustainability of HBMMSs.