Bats are exceptional among mammals for harbouring diverse pathogens and for their robust immune systems. In addition, bats are unusually long-lived and show low rates of cancer. Contiguous and complete reference genomes are needed to determine the genetic basis of these adaptations and establish bats as models for research into mammalian health. Here we sequenced and analysed the genomes of the Jamaican fruit bat (Artibeus jamaicensis) and the Mesoamerican mustached bat (Pteronotus mesoamericanus). We sequenced these two species using a mix of Illumina and Oxford Nanopore Technologies (ONT), assembling draft genomes with some of the highest contig N50s (28-29Mb) of bat genomes to date. Work is in progress to increase the base-level accuracies of these genomes. We conducted gene annotation and identified a set of 10,928 orthologs from bats and mammalian outgroups including humans, rodents, horses, pigs, and dogs. To detect positively selected genes as well as lineage-specific gene gains and losses, we carried out comprehensive branch-site likelihood ratio tests and gene family size analyses. Our analysis found signatures of rapid evolution in the innate immune response genes of bats, and evidence of past infections with diverse viral clades in Artibeus jamaicensis and Pteronotus mesoamericanus. We additionally found evidence of positive selection of tumor suppressors, which may play a role in the low cancer rates, in the most recent common ancestor of bats. These new genomic resources enable insights into the extraordinary adaptations of bats, with implications for mammalian evolutionary studies and public health.