The characterization of de novo mutations in regions of high sequence and structural diversity from whole-genome sequencing data remains highly challenging. Complex structural variants tend to arise in regions of high repetitiveness and low complexity, challenging both de novo assembly, in which short reads do not capture the long-range context required for resolution, and mapping approaches, in which improper alignment of reads to a reference genome that is highly diverged from that of the sample can lead to false or partial calls. Long-read technologies can potentially solve such problems but are currently unfeasible to use at scale. Here we present Corticall, a graph-based method that combines the advantages of multiple technologies and prior data sources to detect arbitrary classes of genetic variant. We construct multisample, colored de Bruijn graphs from short-read data for all samples, align long-read-derived haplotypes and multiple reference data sources to restore graph connectivity information, and call variants using graph path-finding algorithms and a model for simultaneous alignment and recombination. We validate and evaluate the approach using extensive simulations and use it to characterize the rate and spectrum of de novo mutation events in 119 progeny from four Plasmodium falciparum experimental crosses, using long-read data on the parents to inform reconstructions of the progeny and to detect several known and novel nonallelic homologous recombination events.