Unsupervised multimodal semantic discovery aims to learn discriminative representations from multimodal data. However, existing methods suffer from two key limitations. First, they only align instances across modalities without modeling semantic-level consistency, which fails to mitigate semantic bias caused by the gaps among feature distributions of multiple modalities. Second, they inevitably generate incorrect negative pairs during contrastive learning, pushing semantically similar samples apart. To address these challenges, we propose GLAD (Global and Local semantic Alignment for unsupervised multimodal semantic Discovery), which aligns multimodal data at both global and local semantic levels. At the global level, GSA integrates multi-modal features into a shared space and employs joint clustering via optimal transport to capture common semantic patterns while mitigating cross-modality semantic bias. At the local level, LSA adaptively weights samples within each cluster based on their semantic importance, alleviating the effect of incorrect negative pairs. Through the joint optimization of GSA and LSA, GLAD effectively captures both the global semantic structure and the local semantic nuances of multimodal data. Extensive experiments on three benchmark datasets demonstrate GLAD significantly outperforms state-of-the-art methods, with an average improvement of 3.22\%.