The duplication-triplication/inverted-duplication (DUP-TRP/INV-DUP) structure is a complex genomic rearrangement (CGR). Although it has been identified as an important pathogenic DNA mutation signature in genomic disorders and cancer genomes, its architecture remains unresolved. Here, we studied the genomic architecture of DUP-TRP/INV-DUP by investigating the DNA of 24 patients identified by array comparative genomic hybridization (aCGH) on whom we found evidence for the existence of 4 out of 4 predicted structural variant (SV) haplotypes. Using a combination of short-read genome sequencing (GS), long-read GS, optical genome mapping, and single-cell DNA template strand sequencing (strand-seq), the haplotype structure was resolved in 18 samples. The point of template switching in 4 samples was shown to be a segment of ∼2.2–5.5 kb of 100% nucleotide similarity within inverted repeat pairs. These data provide experimental evidence that inverted low-copy repeats act as recombinant substrates. This type of CGR can result in multiple conformers generating diverse SV haplotypes in susceptible dosage-sensitive loci. Display omitted •Inverted triplications cause genomic disorders through alterations in gene dosage•Pairs of homologous inverted repeats generate varying structural haplotypes•Breakpoint junction mapping reveals template switches within repeats•Combining methodologies enhance the analysis of complex genomic aberrations Analysis of 24 individuals harboring inverted triplications show surprising structural variant haplotype diversity and underlie the importance of inverted repeats acting as points of genomic instability leading to genomic disorders.