Two-stage learning pipeline has achieved promising results in unsupervised visible-infrared person re-identification (USL-VI-ReID). It first performs single-modality learning and then operates cross-modality learning to tackle the modality discrepancy. Although promising, this pipeline inevitably introduces modality bias: modality-specific cues learned in the single-modality training naturally propagate into the following cross-modality learning, impairing identity discrimination and generalization. To address this issue, we propose a Dual-level Modality Debiasing Learning (DMDL) framework that implements debiasing at both the model and optimization levels. At the model level, we propose a Causality-inspired Adjustment Intervention (CAI) module that replaces likelihood-based modeling with causal modeling, preventing modality-induced spurious patterns from being introduced, leading to a low-biased model. At the optimization level, a Collaborative Bias-free Training (CBT) strategy is introduced to interrupt the propagation of modality bias across data, labels, and features by integrating modality-specific augmentation, label refinement, and feature alignment. Extensive experiments on benchmark datasets demonstrate that DMDL could enable modality-invariant feature learning and a more generalized model. The code is available at https://github.com/priester3/DMDL.