Hybridization, introgression, and reciprocal gene flow during speciation, specifically the generation of mitonuclear discordance, are increasingly observed as parts of the speciation process. Genomic approaches provide insight into where, when, and how adaptation operates during and after speciation and can measure historical and modern introgression. Whether adaptive or neutral in origin, hybridization can cause mitonuclear discordance by placing the mitochondrial genome of one species (or population) in the nuclear background of another species. The latter, introgressed species may eventually have its own mtDNA replaced or "captured" by other species across its entire geographical range. Intermediate stages in the capture process should be observable. Two nonsister species of Australasian monarch-flycatchers, Spectacled Monarch (Symposiachrus trivirgatus) mostly of Australia and Indonesia and Spot-winged Monarch (S. guttula) of New Guinea, present an opportunity to observe this process. We analysed thousands of single nucleotide polymorphisms (SNPs) derived from ultraconserved elements of all subspecies of both species. Mitochondrial DNA sequences of Australian populations of S. trivirgatus form two paraphyletic clades, one being sister to and presumably introgressed by S. guttula despite little nuclear signal of introgression. Population genetic analyses (e.g., tests for modern and historical gene flow and selection) support at least one historical gene flow event between S. guttula and Australian S. trivirgatus. We also uncovered introgression from the Maluku Islands subspecies of S. trivirgatus into an island population of S. guttula, resulting in apparent nuclear paraphyly. We find that neutral demographic processes, not adaptive introgression, are the most likely cause of these complex population histories. We suggest that a Pleistocene extinction of S. guttula from mainland Australia resulted from range expansion by S. trivirgatus.