The production of hydrogen from offshore wind power is an effective way to fully utilize offshore wind energy and promote low-carbon economic operation in integrated energy system. This paper proposes a multi-level market optimization model for an integrated energy system that includes hydrogen production from offshore wind power. The model considers factors such as wind curtailment penalties and demand response costs. The research focuses on the integration of electrothermal energy systems, hydrogen production, carbon capture storage technology, and a ladder carbon pricing mechanism to establish an optimal operation model for participation in various energy markets and trading platforms. The goal is to maximize economic benefits, ensure system stability, and protect the environment. Simulation results demonstrate that system economic benefits increase by 205.64% when income from hydrogen sales is considered. Additionally, the market price of hydrogen and the capacity of the electrolyzer that meet the system's economic and environmental goals are found to be [1.52 yuan/m3, 3 yuan/m3] and [1500 kW, 1700 kW], respectively. Under the ladder carbon pricing mechanism, the optimal carbon trading parameters are determined to be a base price of 108 yuan/t and a price growth rate of 0.6. The participation of the integrated energy system in multi-level market trading can improve economic efficiency, reduce carbon emissions, utilize offshore wind power fully, and enable the flexible application of energy sources such as hydrogen.