Face Anti-Spoofing (FAS) is crucial for securing face recognition systems against presentation attacks. With advancements in sensor manufacture and multi-modal learning techniques, many multi-modal FAS approaches have emerged. However, they face challenges in generalizing to unseen attacks and deployment conditions. These challenges arise from (1) modality unreliability, where some modality sensors like depth and infrared undergo significant domain shifts in varying environments, leading to the spread of unreliable information during cross-modal feature fusion, and (2) modality imbalance, where training overly relies on a dominant modality hinders the convergence of others, reducing effectiveness against attack types that are indistinguishable by sorely using the dominant modality.To address modality unreliability, we propose the Uncertainty-Guided Cross-Adapter (U-Adapter) to recognize unreliably detected regions within each modality and suppress the impact of unreliable regions on other modalities. For modality imbalance, we propose a Rebalanced Modality Gradient Modulation (ReGrad) strategy to rebalance the convergence speed of all modalities by adaptively adjusting their gradients.Besides, we provide the first large-scale benchmark for evaluating multi-modal FAS performance under domain generalization scenarios. Extensive experiments demonstrate that our method outperforms state-of-the-art methods. Source codes and protocols are released on https://github.com/OMGGGGG/mmdg.