This paper presents a holistic pricing and distributed scheduling framework for multi-microgrid system (MMGS) that considers the supply‒demand relationships of the coupled electricity‒carbon market to promote collaborative market trading within the MMGS for economic and environmental benefit improvement. Initially, an operation model of each microgrid is developed by synthetically considering electricity-carbon operational constraints related to generation units and energy storage units. Then, a collaborative optimization strategy of the MMGS is established according to the Nash bargaining game (NBG) model with the objective of maximizing overall operational revenue. To determine the trading schedule, an accelerated prediction-correction-based alternating direction method of multipliers (PCB-ADMM) algorithm is employed to derive the optimal scheduling strategy of MMGS in a distributed manner, ensuring the privacy preservation of individual microgrids. For electricity-carbon pricing, a supply-demand ratio (SDR) based pricing strategy is proposed to dynamically update electricity and carbon allowance prices, which fundamentally guides and incentivizes each microgrid to trade within the MMGS preferentially rather than with an upstream distribution network. Finally, a study case verifies the effectiveness of the proposed framework in enhancing the operation economy and environmental friendliness of the entire MMGS.