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 simultaneously trains synaptic weights and spike thresholds in SNNs. SNNs trained with synapse-threshold synergistic learning (STL-SNNs) achieve significantly higher accuracies on various static and neuromorphic datasets than SNNs trained with two singlelearning models of the synaptic learning (SL) and the threshold learning (TL). 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 (JDF). 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.