Single-cell RNA sequencing enables the study of biological processes at high resolution, but the high dimensionality and sparsity of its measurements make downstream analyses, such as expression quantitative trait locus (eQTL) mapping, a difficult task. The Latent Interaction Variational Inference (LIVI) model addresses this challenge by learning low-dimensional interpretable embeddings for the cell-state, donor, and donor-cell-state interaction that can be used as phenotypes for association testing. However, LIVI models only gene-expression measurements and does not exploit information from other modalities, such as surface-protein counts that are included in widely used data collection methods such as CITE-seq. In this work, we investigate how LIVI can be extended to jointly model paired RNA and protein data and whether such an extension improves the biological interpretability of its latent representations. We introduce two architectures. Multimodal Shared-space Latent Interaction Variational Inference (MultiSLIVI) is a conservative extension in which RNA and protein measurements share the original cell-state latent space while being reconstructed through modality-specific decoders. Disentangled Multimodal Latent Interaction Variational Inference (DMLIVI) instead separates the cell-state representation into shared and modality-specific components, incorporating disentanglement principles from multimodal variational autoencoders. The models are evaluated using reconstruction performance, cell-type and donor predictability, latent-space structure, and downstream analysis. Most notably, both MultiSLIVI and DMLIVI recover fewer SNP-factor associations than the original LIVI model, indicating that the current multimodal extensions do not improve the donor-factor phenotypes used for eQTL mapping. Nevertheless, the proposed models provide a first step toward multimodal extensions of LIVI and highlight the importance of separating shared and modality-specific variation in future model designs. ... Read more