The surge of distributed renewable energy resources has given rise to the emergence of prosumers, facilitating the low-carbon transition of distribution networks. However, flexible prosumers introduce bidirectional power and carbon interaction, increasing the complexity of practical decision-making in distribution networks. To address these challenges, this paper presents a carbon-coupled network charge-guided bi-level interactive optimization method between the distribution system operator and prosumers. In the upper level, a carbon-emission responsibility settlement method that incorporates the impact of peer-to-peer (P2P) trading is proposed, based on a carbon-emission flow model and optimal power flow model, leading to the formulation of carbon-coupled network charges. In the lower level, a decentralized P2P trading mechanism is developed to achieve the clearing of energy and carbon-emission rights. Furthermore, an alternating direction method of multipliers with an adaptive penalty factor is introduced to address the equilibrium of the P2P electricity–carbon coupled market, and an improved bisection method is employed to ensure the convergence of the bi-level interaction. A case study on the modified IEEE 33-bus system demonstrates the effectiveness of the proposed model and methodology.