Spiking neural networks (SNNs) have demonstrated excellent capabilities in various intelligent scenarios. Most existing methods for training SNNs are based on the concept of synaptic plasticity; however, learning in the realistic brain also utilizes intrinsic non-synaptic mechanisms of neurons. The spike threshold of biological neurons is a critical intrinsic neuronal feature that exhibits rich dynamics on a millisecond timescale and has been proposed as an underlying mechanism that facilitates neural information processing. In this study, we develop a novel synergistic learning approach that involves simultaneously training synaptic weights and spike thresholds in SNNs. SNNs trained with synapse-threshold synergistic learning~(STL-SNNs) achieve significantly superior performance on various static and neuromorphic datasets than SNNs trained with two degenerated single-learning models. During training, the synergistic learning approach optimizes neural thresholds, providing the network with stable signal transmission via appropriate firing rates. Further analysis indicates that STL-SNNs are robust to noisy data and exhibit low energy consumption for deep network structures. Additionally, the performance of STL-SNN can be further improved by introducing a generalized joint decision framework. Overall, our findings indicate that biologically plausible synergies between synaptic and intrinsic non-synaptic mechanisms may provide a promising approach for developing highly efficient SNN learning methods.