Carbon emissions trading is regarded as an effective method that can consider both power economy and low-carbon environmental protection, bringing new features to the conventional multi-microgrid (MMG) day-ahead dispatch. In this paper, a robust decentralized energy management framework for monitoring a collaborative structure of gas turbines (GT), gas boilers (GB), ground source heat pumps (GSHP), energy storage (ES), and electrolyzers for a microgrid (MG) in the presence of power-to-gas (P2G) and carbon capture systems is proposed (CCS). Demand response (DR) is presented as a means of improving the system’s flexibility to multiple energy demands. As MMG are sensitive to price fluctuations, the robust optimization model can manage uncertainty by considering the worst-case scenario for trading prices at varying conservative levels. The Kalman filter (KF) distributed algorithm based on iteration is utilized to decompose the dispatch problem to minimize the total daily overhead of the MMG system while protecting the privacy of MG data. In conclusion, the simulation results demonstrate the ability of the proposed decentralized model to meet the demand for electricity and heat under the worst-case scenario of electricity pricing.