Profiling of gene expression and chromatin accessibility by single-cell multi-omics approaches can help to systematically decipher how transcription factors (TFs) regulate target gene expression via cis-region interactions. However, integrating information from different modalities to discover regulatory associations is challenging, in part because motif scanning approaches miss many likely TF binding sites. We develop REUNION, a framework for predicting genome-wide TF binding and cis-region-TF-gene "triplet" regulatory associations using single-cell multi-omics data. The first component of REUNION, Unify, utilizes information theory-inspired complementary score functions that incorporate TF expression, chromatin accessibility, and target gene expression to identify regulatory associations. The second component, Rediscover, takes Unify estimates as input for pseudo semi-supervised learning to predict TF binding in accessible genomic regions that may or may not include detected TF motifs. Rediscover leverages latent chromatin accessibility and sequence feature spaces of the genomic regions, without requiring chromatin immunoprecipitation data for model training. Applied to peripheral blood mononuclear cell data, REUNION outperforms alternative methods in TF binding prediction on average performance. In particular, it recovers missing region-TF associations from regions lacking detected motifs, which circumvents the reliance on motif scanning and facilitates discovery of novel associations involving potential co-binding transcriptional regulators. Newly identified region-TF associations, even in regions lacking a detected motif, improve the prediction of target gene expression in regulatory triplets, and are thus likely to genuinely participate in the regulation. All source code is available at https://github.com/yangymargaret/REUNION.