Logged tropical forests can retain a great deal of biodiversity, but there is substantial variation in the type and severity of habitat degradation caused by logging. Logging-induced habitat degradation can vary significantly at fine spatial scales, with differing effects on plant communities and the growth of lianas, which are woody, climbing vines that proliferate in degraded forests and infest trees by climbing onto them and competing for above and below ground resources. The impacts of such fine-scale variation in habitat structure on faunal diversity is relatively poorly known. We recorded soundscapes and variation in local-scale habitat structure in selectively logged and old-growth primary forests in Malaysian Borneo to examine how changes to logged forest structure predict variation in acoustic diversity indices that are known to correlate with biodiversity indices. We show that acoustic indices relating to higher soundscape diversity increase with liana prevalence but decline with tree species richness and are unaffected by the liana load of adult trees. Our results suggest that acoustic data represent a simple, practicable measure for detecting fine-scale patterns of biodiversity response to post-logging habitat structure. Our findings also suggest that retaining many trees lightly infested by lianas in logged forests is the optimal outcome for biodiversity. This emphasises the need for forest restoration that retains some climbers, rather than blanket-cutting of all stems in projects seeking to return post-logging forest communities towards their primary forest state.