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Achieving high-fidelity audio compression while preserving perceptual quality across diverse audio types remains a significant challenge in Neural Audio Coding (NAC). This paper introduces MUFFIN, a fully convolutional NAC framework that leverages psychoacoustically guided multi-band frequency reconstruction. Central to MUFFIN is the Multi-Band Spectral Residual Vector Quantization (MBS-RVQ) mechanism, which quantizes latent speech across different frequency bands. This approach optimizes bitrate allocation and enhances fidelity based on psychoacoustic studies, achieving efficient compression with unique perceptual features that separate content from speaker attributes through distinct codebooks. MUFFIN integrates a transformer-inspired convolutional architecture with proposed modified snake activation functions to capture fine frequency details with greater precision. Extensive evaluations on diverse datasets (LibriTTS, IEMOCAP, GTZAN, BBC) demonstrate MUFFIN’s ability to consistently surpass existing performance in audio reconstruction across various domains. Notably, a high-compression variant achieves an impressive SOTA 12.5 kHz rate while preserving reconstruction quality. Furthermore, MUFFIN excels in downstream generative tasks, demonstrating its potential as a robust token representation for integration with large language models. These results establish MUFFIN as a groundbreaking advancement in NAC and as the first neural psychoacoustic coding system. Speech demos and codes are available at \url{https://demos46.github.io/muffin/} and \url{https://github.com/dianwen-ng/MUFFIN}.