Nowadays, deep learning-based joint source-channel coding (JSCC) is getting attention, and it shows excellent performance compared with separate source and channel coding (SSCC). However, most JSCC works are only designed, trained, and tested on additive white Gaussian noise (AWGN) channels to transmit analog signals. In current communication systems, digital signals are considered more. Hence, it is necessary to design an end-to-end JSCC framework for digital signal transmission. In this paper, we propose a digital JSCC framework (S-JSCC) based on spiking neural network (SNN) to tackle this problem. The SNN is used to compress the feature of the deep model, and the compressed results are transmitted over digital channels such as binary symmetric channel (BSC) and binary erasure channel (BEC). Since the outputs of SNN are binary spikes, the framework can be applied directly to digital channels without extra quantization. Moreover, we propose a new spiking neuron and regularization method to improve the performance and robustness of the system. The experimental results show that under digital channels, the proposed S-JSCC framework performs better than the state-of-the-art convolution neural network (CNN)-based JSCC framework, which needs extra quantization.