Face normalization aims to enhance the robustness and effectiveness of face recognition systems by mitigating intra-personal variations in expressions, poses, occlusions, illuminations, and domains. Existing methods face limitations in handling multiple variations and adapting to cross-domain scenarios. To address these challenges, we propose a novel Unified Multi-Domain Face Normalization Network (UMFN) model, which can process face images with various types of facial variations from different domains, and reconstruct frontal, neutral-expression facial prototypes in the target domain. As an unsupervised domain adaptation model, UMFN facilitates concurrent training on multiple datasets across domains and demonstrates strong prototype reconstruction capabilities. Notably, UMFN serves as a joint prototype and feature learning framework, enabling the simultaneous extraction of domain-agnostic identity features through a decoupling mapping network and a feature domain classifier for adversarial training. Moreover, we design an efficient Heterogeneous Face Recognition (HFR) network that fuses domain-agnostic and identity-discriminative features for HFR, and introduce contrastive learning to enhance identity recognition accuracy. Empirical studies on diverse cross-domain face datasets validate the effectiveness of our proposed method.