A low-carbon economic dispatch model for an integrated energy system (IES) is proposed under the "dual-carbon" policy framework to promote green and low-carbon energy transition. This model incorporates a green certificate-carbon trading joint mechanism and hybrid game theory. Firstly, a two-layer hybrid game model is constructed. In the upper-layer model, the system operator is treated as the leader, and energy purchase and sale pricing strategies are formulated to maximize its own profit. In the lower-layer model, the hydrogen multi-energy integrated energy system (HMIES) alliance is considered as the follower, and its output is optimized to achieve the best overall economic performance for the alliance. Secondly, a green certificate-carbon joint trading mechanism is introduced into the cooperative game model of the HMIES alliance to improve the overall low-carbon economic performance. Cooperative game theory is applied to analyze the conditions for cooperation, and the Shapley value method is used to allocate cooperative surplus fairly. This enables collaborative interaction between carbon capture power plants and renewable energy generators within the alliance. Lastly, the model is solved using a genetic algorithm combined with mixed integer linear programming (GA-MILP). Case simulations are conducted to verify the effectiveness of the proposed strategy. The results demonstrate that carbon emissions are effectively reduced, and system economic performance is improved.