The Integrated Energy System (IES) multifaceted load forecasting technology is a critical foundation for ensuring the balance and stable operation of the system supply and demand. Due to the complex coupling relationships among various loads, this paper constructs a regional IES multifaceted load forecasting model based on the Grey Relation Analysis (GRA) method and the Bi-directional Long Short-Term Memory (BI-LSTM) neural network to delve into the coupling characteristics between electric, thermal, and cooling loads. Firstly, the Grey Relation Analysis is employed to analyze the correlation of multifaceted loads, determining the prediction priority of multifaceted loads in the integrated energy system. Secondly, based on the exploration of coupling characteristics among multifaceted loads, the k-means clustering algorithm is applied to partition loads with the highest priority into sets with similar fluctuations. Finally, for each load scenario set, a hierarchical prediction strategy is implemented using the BI-LSTM network for scenario set prediction modeling. Case study results indicate that the proposed forecasting model exhibits high prediction accuracy and effectively handles the intense fluctuations in loads, meeting the operational requirements for the system's safety and stability.