Data hiding is essential for secure communication across digital media, and recent advances in Deep Neural Networks (DNNs) provide enhanced methods for embedding secret information effectively. However, previous audio hiding methods often result in unsatisfactory quality when recovering secret audio, due to their inherent limitations in the modeling of time-frequency relationships. In this paper, we explore these limitations and introduce a new DNN-based approach. We use a flow-based invertible neural network to establish a direct link between stego audio, cover audio, and secret audio, enhancing the reversibility of embedding and extracting messages. To address common issues from time-frequency transformations that degrade secret audio quality during recovery, we implement a time-frequency loss on the time-domain signal. This approach not only retains the benefits of time-frequency constraints but also enhances the reversibility of message recovery, which is vital for practical applications. We also add an encryption technique to protect the hidden data from unauthorized access. Experimental results on the VCTK and LibriSpeech datasets demonstrate that our method outperforms previous approaches in terms of subjective and objective metrics and exhibits robustness to various types of noise, suggesting its utility in targeted secure communication scenarios.