Facial action units (AUs), as defined in the Facial Action Coding System (FACS), have received significant research interest owing to their diverse range of applications in facial state analysis. Current mainstream FAU recognition models have a notable limitation, i.e., focusing only on the accuracy of AU recognition and overlooking explanations of corresponding AU states. In this paper, we propose an end-to-end Vision-Language joint learning network for explainable FAU recognition (termed VL-FAU), which aims to reinforce AU representation capability and language interpretability through the integration of joint multimodal tasks. Specifically, VL-FAU brings together language models to generate fine-grained local muscle descriptions and distinguishable global face description when optimising FAU recognition. Through this, the global facial representation and its local AU representations will achieve higher distinguishability among different AUs and different subjects. In addition, multi-level AU representation learning is utilised to improve AU individual attention-aware representation capabilities based on multi-scale combined facial stem feature. Extensive experiments on DISFA and BP4D AU datasets show that the proposed approach achieves superior performance over the state-of-the-art methods on most of the metrics. In addition, compared with mainstream FAU recognition methods, VL-FAU can provide local- and global-level interpretability language descriptions with the AUs' predictions.