Multimodal Face Anti-Spoofing (FAS) methods, which integrate multiple visual modalities, often suffer even more severe performance degradation than unimodal FAS when deployed in unseen domains. This is mainly due to two overlooked risks that affect cross-domain multimodal generalization. The first is the modal representation invariant risk, i.e., whether representations remain generalizable under domain shift. We theoretically show that the inherent class asymmetry in FAS (diverse spoofs vs. compact reals) enlarges the upper bound of generalization error, and this effect is further amplified in multimodal settings. The second is the modal synergy invariant risk, where models overfit to domain-specific inter-modal correlations. Such spurious synergy cannot generalize to unseen attacks in target domains, leading to performance drops. To solve these issues, we propose a provable framework, namely Multimodal Representation and Synergy Invariance Learning (RiSe). For representation risk, RiSe introduces Asymmetric Invariant Risk Minimization (AsyIRM), which learns an invariant spherical decision boundary in radial space to fit asymmetric distributions, while preserving domain cues in angular space. For synergy risk, RiSe employs Multimodal Synergy Disentanglement (MMSD), a self-supervised task enhancing intrinsic, generalizable modal features via cross-sample mixing and disentanglement. Theoretical analysis and experiments verify RiSe, which achieves state-of-the-art cross-domain performance.