Discrete audio representations are gaining traction in speech modeling due to their interpretability and compatibility with large language models, but are not always optimized for noisy or real-world environments. Building on existing works that quantize Whisper embeddings for speech-to-unit modeling, we propose disentangling semantic speech content from background noise in the latent space. Our end-to-end model separates clean speech in the form of codebook tokens, while extracting interpretable noise vectors as quantization residue which are supervised via a lightweight classifier. We show that our approach improves alignment between clean/noisy speech and text, producing speech tokens that display a high degree of noiseinvariance, and improves ASR performance. Keeping Whisper frozen, we show an 82% reduction in error rate compared to Whisper, and 35% improvement over baseline methods on the VBDemand test set. Further analyses show that the learned token space generalizes well to both seen and unseen acoustic conditions.