Guided by the “dual carbon” goal, the AC/DC hybrid distribution network has gradually become an important direction for the future development of the distribution system. However, a certain contradiction exists between the two major demands of carbon reduction and improvement of power network resilience, and their efficient coordination is hampered. In view of this, a collaborative optimization method for AC/DC hybrid distribution networks based on approximate Nash equilibrium is proposed. Firstly, the impact of carbon reduction and resilience on the operation of AC/DC distribution networks under different conditions is explored. Subsequently, a collaborative regulation model considering carbon emissions reduction is proposed, and a measurement index for resilience evaluation is proposed. Based on this, an approximate Nash equilibrium strategy for optimized operation is designed. Ultimately, with the optimization goals of achieving balanced carbon reduction, economy, and resilience, an optimization and control model for the AC/DC hybrid distribution network is constructed. The effectiveness and feasibility of the proposed method in reducing carbon emissions, improving economic efficiency and resilience are verified through improved IEEE33-node examples and a certain park example in Xiong'an New Area.