A complete understanding of biological processes requires synthesizing information across heterogeneous modalities, such as age, disease status, or gene expression. Technological advances in single-cell profiling have enabled researchers to assay multiple modalities simultaneously. We present Schema, which uses a principled metric learning strategy that identifies informative features in a modality to synthesize disparate modalities into a single coherent interpretation. We use Schema to infer cell types by integrating gene expression and chromatin accessibility data; demonstrate informative data visualizations that synthesize multiple modalities; perform differential gene expression analysis in the context of spatial variability; and estimate evolutionary pressure on peptide sequences.