Multimodal learning aims to capture both shared and private information from multiple modalities. However, existing methods that project all modalities into a single latent space for fusion often overlook the asynchronous, multi-level semantic structure of multimodal data. This oversight induces semantic misalignment and error propagation, thereby degrading representation quality. To address this issue, we propose Cross-Level Co-Representation (CLCR), which explicitly organizes each modality's features into a three-level semantic hierarchy and specifies level-wise constraints for cross-modal interactions. First, a semantic hierarchy encoder aligns shallow, mid, and deep features across modalities, establishing a common basis for interaction. And then, at each level, an Intra-Level Co-Exchange Domain (IntraCED) factorizes features into shared and private subspaces and restricts cross-modal attention to the shared subspace via a learnable token budget. This design ensures that only shared semantics are exchanged and prevents leakage from private channels. To integrate information across levels, the Inter-Level Co-Aggregation Domain (InterCAD) synchronizes semantic scales using learned anchors, selectively fuses the shared representations, and gates private cues to form a compact task representation. We further introduce regularization terms to enforce separation of shared and private features and to minimize cross-level interference. Experiments on six benchmarks spanning emotion recognition, event localization, sentiment analysis, and action recognition show that CLCR achieves strong performance and generalizes well across tasks.