With the ongoing low-carbon transition in the energy sector, integrated energy systems have received extensive attention for their multi-energy complementary and potential for facilitating renewable energy consumption. To reflect the market value of such systems, participation in electricity, gas, carbon, green certificate multi-markets competition has become an emerging trend. As the main competitive entities bidding in these markets, the strategic behaviors of integrated energy suppliers’ (IES) can significantly impacts on market outcomes. Therefore, a joint equilibrium model of electricity- gas-carbon-green certificate markets with IES participation including renewable units is constructed. The model captures the game-theoretic interactions between IESs and single-energy suppliers across four interdependent markets. The uncertainty of renewable energy output is also taken into consideration, and a deviation penalty mechanism is introduced to deal with bidding deviations from renewable units. The nonlinear complementarity approach is applied to solve this joint equilibrium model. Finally, numerical examples are presented to validate the rationality and effectiveness of the proposed model. The results show that, compared to cases without the introduction of the carbon and green certificate markets, IESs’ participation in the electricity-gas-carbon-green certificate markets can increase profits by 6.5% and decrease carbon emissions by 7.2%.