Natural hybrid zones can be used to dissect the mechanisms driving key evolutionary processes by allowing us to identify genomic regions important for establishing reproductive isolation and that allow for transfer of adaptive variation. We leverage whole-genome data in a system where two bird species, the saltmarsh (Ammospiza caudacutus) and Nelson’s (A. nelsoni) sparrow, hybridize despite their relatively high background genetic differentiation and past ecological divergence. Adaptive introgression is plausible in this system because Nelson’s sparrows are recent colonists of saltwater marshes, compared to the specialized saltmarsh sparrow that has a longer history of salt-marsh adaptation. Comparisons among whole-genome sequences of 34 individuals from allopatric and sympatric populations show that ongoing gene flow is shaping the genomic landscape, with allopatric populations exhibiting genome-wide FST estimates close to double of that observed in sympatry. We characterized patterns of introgression across the genome and identify regions that exhibit biased introgression into hybrids from only one parental species. These regions offer compelling candidates for genes related to tidal marsh adaptations suggesting that adaptive introgression is an important consequence of hybridization. These findings highlight the value of considering the landscapes of both genome-wide introgression and divergence when characterizing the evolutionary forces that drive speciation.