In recent years, emotion recognition based on physiological signals such as electroencephalogram (EEG) has gained considerable attention, as internal physiological data offer greater objectivity and reliability compared to external behavioral data like facial expressions. However, due to distribution shifts caused by individual and contextual differences, along with variations in sample quality across modalities, constructing a cross-domain multimodal emotion recognition model with high generalization and robustness remains a key challenge. In this study, we propose a Unified Framework with Adaptive Multimodal Alignment (UF-AMA) to address cross-subject and cross-session emotion recognition using multimodal physiological signals. First, we construct a cross-modal feature fusion network comprising Transformer encoders and multi-head cross-attention modules, enabling the deep integration of EEG signals and eye-tracking data. Subsequently, we introduce a confidence-aware screening mechanism that dynamically assesses the predictive reliability of each modality branch on target domain samples, partitions samples into different quality subsets, and accordingly applies global consistency alignment and cross-modal distillation. Finally, we propose a multi-level domain adaptation framework that jointly optimizes the marginal and conditional distributions of both local modality-specific and global fusion features, thereby reducing cross-domain distribution shifts at multiple granularities. Extensive experiments on the SEED and SEED-IV datasets demonstrate that UF-AMA achieves state-of-the-art (SOTA) performance in both cross-subject and cross-session tasks. The source code is available at: https://github.com/BetterCoderLab/UF-AMA.