Personalized recommendation requires capturing the complex latent intents underlying user-item interactions. Existing structural models, however, often fail to preserve perspective-dependent interaction semantics and provide only indirect supervision for aligning user and item intents, lacking explicit interaction-level constraints. This entangles heterogeneous interaction signals, leading to semantic ambiguity, reduced robustness under sparse interactions, and limited interpretability. To address these issues, we propose DMICF, a Dual-Perspective Disentangled Multi-Intent framework for collaborative filtering. DMICF models interactions from complementary user- and item-centric perspectives and employs a macro-micro prototype-aware variational encoder to disentangle fine-grained latent intents. Interaction-level supervision enforces dimension-wise alignment between user and item intents, grounding latent factors and enabling their collaborative emergence. Importantly, each component is architecturally flexible, and performance is robust to specific module instantiations. We offer a theoretical analysis to help explain how prototype-aware conditioning may alleviate posterior collapse, while the reconstruction objective promotes intent-wise contrastive alignment between positive and negative interactions. Extensive experiments on multiple benchmarks demonstrate consistent improvements over strong baselines, with ablations validating each core component.