Against the backdrop of China's ''carbon emission peak and carbon neutrality'' goals, the low-carbon transformation of the integrated energy system (IES) is imperative. However, the uncertainties in renewable energy output and load demand, as well as the correlation characteristics between sources and loads and among different loads, pose significant challenges to the configuration and optimization of the system. To address this, a low-carbon configuration and optimization method for IES considering source-load correlation is proposed. Firstly, a flexible carbon capture power plant and a multi-utilization structure for hydrogen energy are introduced to carry out the low-carbon transformation of the IES, constructing a coupled operational model for various devices. Secondly, a sample matrix considering source-load correlation is generated using the Nataf transformation combined with Latin hypercube sampling and singular value decomposition. The final typical source-load scenarios are then obtained through the K-means clustering algorithm. On this basis, a bi-level optimization configuration model for the IES is established. The planning level aims to minimize the system's annualized comprehensive cost, while the operational level focuses on minimizing the system's total annual operating cost. The dual-level model is solved using an iterative approach that combines particle swarm optimization with mixed-integer linear programming. The results of the case study indicate that the configuration considering source-load correlation is more reasonable. A rational allocation of the flexible carbon capture and hydrogen multi-utilization structure can effectively enhance the low-carbon economy of the IES.