At this stage, the concept of low-carbon development is particularly important in order to fully realize the optimal operation of the integrated energy system. This paper proposes an integrated energy dispatching model for electricity and heat that takes into account the effects of uncertainty on both the source and load sides, with the aim of promoting energy saving and emission reduction on the demand side. Based on the actual carbon emissions of the system equipment, a reward and punishment ladder-type carbon trading mechanism that allocates carbon emission allowances to the system at no cost. A deterministic model of integrated electricity-thermal energy dispatch is developed with the objective of minimizing the total system operating costs. A robust scheduling model considering source load uncertainty is developed based on information-gap decision theory under a risk-averse strategy. By setting up different scenarios for analysis, it is demonstrated that reward and punishment ladder-type carbon trading can constrain carbon emissions of the system to a greater extent and synergize the low carbon and economic performance of system. Meanwhile, consideration of source load uncertainty also increases the risk tolerance of the system and makes it more stable.