Chromosomal inversions are fundamental drivers of genome evolution. In the main Afrotropical malaria vector species, belonging to the Anopheles gambiae species complex, inversions play an important role in local adaptation and have a rich history of cytological study. Despite the importance and ubiquity of some chromosomal inversions across the species complex, inversion breakpoints are often challenging to map molecularly due to the presence of large repetitive regions. Here, we develop an approach that uses Hi-C sequencing data to molecularly fine-map the breakpoints of inversions. We demonstrate that this approach is robust and likely to be widely applicable for both identification and fine-mapping inversion breakpoints in species whose inversions have heretofore been challenging to characterize. Furthermore, we propose a method for estimating breakpoint mapping confidence intervals. We apply our method to interrogate the previously unknown inversion breakpoints of 2Rbc and 2Rd in An. coluzzii. We found that inversion breakpoints occur in large repetitive regions, and strikingly among three inversions analyzed, two breakpoints appear to be reused in two separate inversions. These breakpoint-adjacent regions are strongly enriched for the presence of a 30 bp satellite repeat sequence. Because rare inversion breakpoints are not significantly correlated with satellite repeat-containing genomic regions, we suggest that interrupting this particular repeat may result in arrangements with higher relative fitness. Additionally, we use heterozygous individuals to quantitatively investigate the impacts of somatic pairing in the regions immediately surrounding inversion breakpoints. Finally, we discuss important considerations for possible applications of this approach for inversion breakpoint identification in a range of organisms.