Transcriptional enhancers control spatiotemporal gene expression and commonly engage in long-range chromosomal contacts with gene promoters. However, the relationship between enhancer activity, enhancer-promoter contact and gene expression is not completely understood. Here, we leverage human genetic variation as a "natural perturbation" to dissect this relationship. Focusing on enhancers that harbour genetic variants showing allelic associations with the expression levels of distal genes (expression quantitative trait loci, eQTLs), we profiled eQTL-promoter contacts using high-resolution Capture Hi-C, as well as chromatin activity by ATAC-sequencing, in primary monocytes isolated from 34 healthy donors. To detect the associations of genetic variants with these molecular phenotypes, we extended a recently proposed Bayesian method that leverages both intra- and interindividual variation. We identified 19 eQTLs associated with differential promoter contacts, most of which also showed an association with chromatin activity. Capitalising on this overlap, we next adapted a Bayesian mapping strategy for detecting variants that exert genetic control across multiple phenotypes, revealing hundreds of putative "trimodal QTL" variants jointly associated with enhancer activity, connectivity, and gene expression. A subset of these variants was predicted to affect the binding of a diverse range of transcription factors, in part through disruption of the binding motifs for either these factors or their binding partners. In addition, we identified a variant with opposite effects on promoter contact and expression levels of its target gene, PCK2. We show that this variant disrupts the canonical binding motif of the architectural protein CTCF and likely perturbs the chromatin insulation of the PCK2 promoter from more distal enhancers. Finally, multiple identified QTLs overlapped known disease susceptibility loci, pointing to the potential role of enhancer-promoter communication in mediating the pathological effects of non-coding genetic variation. Jointly, our findings suggest an inherent functional link between the activity and connectivity of enhancers with relevance for human disease and highlight the role of genetically-determined chromatin boundaries in gene expression control.