Mechanisms that suppress recombination are known to help maintain species barriers by preventing the breakup of co-adapted gene combinations. The sympatric butterfly species H. melpomene and H. cydno are separated by many strong barriers, but the species still hybridise infrequently in the wild, with around 40% of the genome influenced by introgression. We tested the hypothesis that genetic barriers between the species are reinforced by inversions or other mechanisms to reduce between-species recombination rate. We constructed fine-scale recombination maps for Panamanian populations of both species and hybrids to directly measure recombination rate between these 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.