In the context of the 'dual-carbon' goal, a dual demand response within each microgrid and a cooperative peer-to-peer (P2P) scheduling strategy among microgrids are proposed to build a fairer, green, and low-carbon new electricity market. Firstly, a microgrid model incorporating integrated electricity, heat and gas is constructed, with explicit modeling of flexible loads such as electric vehicles (EVs). Then, the optimization strategies for electricity sharing among multiple microgrids and within microgrids are proposed. At the multi-microgrid level, an optimal scheduling model based on Nash bargaining theory is established, aiming to achieve the optimal benefits for both individual microgrids and the entire microgrid group after their participation in P2P collaboration. Within each microgrid, a dual demand response optimal scheduling model based on dynamic tariffs and EV carbon quota is established with the objective of reducing the microgrid carbon emissions, the peak-to-valley difference of the electric loads, and the charging cost of EVs. Finally, simulation results demonstrate that the proposed optimal scheduling strategy effectively enhances energy sharing and renewable energy consumption among microgrids, and further reduces the system carbon emissions.