Hydrogen-containing integrated energy system is an important component of the future energy system, and the synergistic control of multiple types of electrolyser modules can help to improve the consumption of new energy and the operation efficiency of hydrogen production module. In this paper, the dynamic efficiency and start-stop characteristics of alkaline water electrolyser and proton exchange membrane water electrolyser are modelled, and the operation framework and co-optimization strategy of the electric-hydrogen-thermal integrated energy system with multiple types of electrolyser modules are proposed to achieve the optimization of start-stop and power of each electrolyser module with the goal of minimizing the comprehensive cost consisting of the system operation and maintenance cost, the cost of discarded energy, the cost of starting and stopping the electrolyser, and the revenue from hydrogen production. The operation framework and optimisation strategy proposed in this paper can improve the new energy consumption rate, increase the energy efficiency of the hydrogen production system by 8.13%, and increase the total cost benefit by 40.83%, as verified by the modified IEEE 39-node power-6-node thermal system.