One outcome of interspecific hybridization and subsequent effects of evolutionary forces is introgression, which is the integration of genetic material from one species into the genome of an individual in another species. The evolution of several groups of eukaryotic species has involved hybridization, and cases of adaptation through introgression have been already established. In this work, we report on a new comparative genomic framework for detecting introgression in genomes, called PhyloNet-HMM. The framework combines phylogenetic networks, which capture reticulate evolutionary relationships among genomes, with hidden Markov models (HMMs), which capture dependencies within genomes. A novel aspect of our work is that it also accounts for incomplete lineage sorting and dependence across loci. We validate the performance of PhyloNet-HMM using simulated and empirical data sets which include either tree-like or non-tree-like evolutionary scenarios. Application of our model to variation data from the mouse genome detects a recently reported adaptive introgression event in addition to other newly detected introgression regions. Our work provides a powerful framework for systematic analysis of introgression while simultaneously accounting for dependence across sites, point mutations, recombination, and ancestral polymorphism.