In music recommendation systems, multimodal interest learning is pivotal, which allows the model to capture nuanced preferences, including textual elements such as lyrics and various musical attributes such as different instruments and melodies. Recently, methods that incorporate multimodal content features through semantic IDs have achieved promising results. However, existing methods suffer from two critical limitations: 1) intra-modal semantic degradation, where residual-based quantization processes gradually decouple discrete IDs from original content semantics, leading to semantic drift; and 2) inter-modal modeling gaps, where traditional fusion strategies either overlook modal-specific details or fail to capture cross-modal correlations, hindering comprehensive user interest modeling. To address these challenges, we propose a novel multimodal recommendation framework with two stages. In the first stage, our Progressive Semantic Residual Quantization (PSRQ) method generates modal-specific and modal-joint semantic IDs by explicitly preserving the prefix semantic feature. In the second stage, to model multimodal interest of users, a Multi-Codebook Cross-Attention (MCCA) network is designed to enable the model to simultaneously capture modal-specific interests and perceive cross-modal correlations. Extensive experiments on multiple real-world datasets demonstrate that our framework outperforms state-of-the-art baselines. This framework has been deployed on one of China's largest music streaming platforms, and online A/B tests confirm significant improvements in commercial metrics, underscoring its practical value for industrial-scale recommendation systems.