Tau positron emission tomography (tau-PET) is an important in vivo biomarker of Alzheimer's disease, but its cost, limited availability, and acquisition burden restrict broad clinical use. This work proposes an interpretable multimodal image synthesis framework for generating tau-PET from paired T1-weighted and FLAIR MRI. The proposed model combines a Partial Information Decomposition-inspired vector-quantized encoder, which separates latent representations into redundant, unique, and complementary (synergistic) components, with a Half-UNet decoder that preserves anatomical structure through edge-conditioned pseudo-skip connections rather than direct encoder-to-decoder feature bypass. The method was evaluated on 605 training and 83 validation subjects from ADNI-3 and OASIS-3 and compared against continuous-latent, discrete-latent, and direct-regression baselines, including VAE, VQ-VAE, UNet, and SPADE-based UNet variants. Evaluation included raw PET reconstruction, SUVR reconstruction, high-uptake region preservation, regional agreement, Braak-stage tracking, and post-hoc statistical testing. Across 17 evaluated models, the proposed DQ2H-MSE-Inf variant achieved the best raw PET fidelity and the strongest downstream Braak-stage performance, while remaining competitive on SUVR reconstruction and regional agreement. Shapley analysis further showed that complementary and redundant latent components contributed the largest gains, supporting the role of cross-modal interaction in tau-PET recovery. We show that our method can support clinically relevant tau-PET synthesis while providing improved architectural interpretability.