Multienergy loads in integrated energy systems (IESs) exhibit strong volatility and randomness, and existing multitask sharing methods often encounter negative migration and seesaw problems when addressing complexity and competition among loads. In line with these considerations, a short-term multienergy load joint prediction method based on seasonal-trend decomposition using LOESS (STL) and convolutional progressive layered extraction (CPLE) is proposed, called STL-CPLE. First, STL is applied to model regular and uncertain load information into interpretable trend, seasonal, and residual components. Then, joint modeling is performed for the same type of components of multienergy loads. A one-dimensional convolutional neural network (1DCNN) is constructed to extract deeper feature information. This approach works in concert with the progressive layered extraction sharing method, and convolutional shared and task-specific experts are developed to acquire common and distinctive representations of multienergy loads, respectively. Task-specific parameters are gradually separated through progressive routing. Finally, a subtask network is built to learn temporal dependencies using long short-term memory (LSTM). Simulation validation is performed on the IES dataset at the Tempe campus of Arizona State University, and the experiments show that the STL-CPLE method exhibits higher prediction accuracy than do the other methods.