Accurate multi-energy load forecasting plays an important role in the stable and secure operation of integrated energy systems (IESs). The strong randomness and complex coupling relationship among multiple energy loads bring huge challenges for the accurate forecasting of multi-energy load. In this context, this paper proposes a multi-task learning method-enabled probabilistic load forecasting method for the joint prediction of electric, cooling, and heating loads. Specifically, a complex neural network (ComNN) is developed to capture the coupling relationships between the multiple loads by taking aggregated multi-source information as input. The hard-parameter sharing mechanism is adopted to share information between tasks and reduce the risk of overfitting in multi-task learning. To balance the training of multiple loads, a geometric loss function (GLF) is designed for the optimization of the ComNN. It is further extended to a geometric quantile loss function to capture the uncertainties of multi-energy load. The ComNN allows the coupling information to be shared among the multiple tasks, which enhances the forecasting performance of the proposed method on each individual task. The designed geometric quantile loss function further enables the proposed method to dynamically balance the weights for different tasks during training and achieve effective quantification of the multi-energy load forecasting outcomes. Comparative tests with state-of-the-art forecasting methods using regional IES load data from Arizona State University's Tempe campus and Western China demonstrate the effectiveness of the proposed method in both deterministic and probabilistic multi-energy load forecasting.