End-to-end speech-to-text translation (E2E-ST) is becoming increasingly popular due to the potential of its less error propagation, lower latency, and fewer parameters. Given the triplet training corpus $\langle speech, transcription, translation\rangle$, the conventional high-quality E2E-ST system leverages the $\langle speech, transcription\rangle$ pair to pre-train the model and then utilizes the $\langle speech, translation\rangle$ pair to optimize it further. However, this process only involves two-tuple data at each stage, and this loose coupling fails to fully exploit the association between triplet data. In this paper, we attempt to model the joint probability of transcription and translation based on the speech input to directly leverage such triplet data. Based on that, we propose a novel regularization method for model training to improve the agreement of dual-path decomposition within triplet data, which should be equal in theory. To achieve this goal, we introduce two Kullback-Leibler divergence regularization terms into the model training objective to reduce the mismatch between output probabilities of dual-path. Then the well-trained model can be naturally transformed as the E2E-ST models by the pre-defined early stop tag. Experiments on the MuST-C benchmark demonstrate that our proposed approach significantly outperforms state-of-the-art E2E-ST baselines on all 8 language pairs, while achieving better performance in the automatic speech recognition task. Our code is open-sourced at https://github.com/duyichao/E2E-ST-TDA.