<p>Robust watermarking, as a key technology for speech legitimacy authentication, is increasingly adopting deep learning methods to enhance its performance. Current critical challenges in robust watermarking include: how to enhance the payload capacity of robust watermarking based on deep learning (DL-RW), how to maintain good robustness against all content preserving operations. Existing DL-RW often exhibit extremely low payload capacity, sometimes even below 20 bps. Furthermore, existing robust watermarking methods demonstrate poor robustness against certain attacks, such as noise addition. These issues limit the application of digital watermarking in legitimacy authentication. To address these issues, this paper proposes a multi-band robust watermarking method based on the Invertible Neural Network (INN). This method embeds watermarking into multiple frequency bands of the DWT using INN, effectively enhancing the payload capacity. Subsequently, based on the characteristics of robust watermarking, a progressive curriculum learning strategy is applied during training to separately develop the fundamental functionality and robustness of the watermarking. Finally, a synchronization and error correction (S-EC) mechanism is proposed to encode target information into watermarking, achieving synchronization of watermarking and error correction of target information during the decoding phase. Experimental results indicate that the proposed multi-band robust watermarking has a payload capacity of 120 bps, with 40 bps per band. The proposed progressive curriculum learning strategy fully unleashes the performance of INN in robust watermarking, enabling the method to maintain high transparency and robustness while maintaining large payload capacity. The average BER under common attacks is 1.32% and SNR is 26.5156 dB. The average BER after applying the S-EC mechanism is 0.30%.</p>