Mechanisms that suppress recombination are known to help maintain species barriers by preventing the breakup of coadapted gene combinations. The sympatric butterfly species Heliconius melpomene and Heliconius cydno are separated by many strong barriers, but the species still hybridize infrequently in the wild, and around 40% of the genome is influenced by introgression. We tested the hypothesis that genetic barriers between the species are maintained by inversions or other mechanisms that reduce between-species recombination rate. We constructed fine-scale recombination maps for Panamanian populations of both species and their hybrids to directly measure recombination rate within and between species, and generated long sequence reads to detect inversions. We find no evidence for a systematic reduction in recombination rates in F1 hybrids, and also no evidence for inversions longer than 50 kb that might be involved in generating or maintaining species barriers. This suggests that mechanisms leading to global or local reduction in recombination do not play a significant role in the maintenance of species barriers between H. melpomene and H. cydno.