Baobabs (Adansonia) are a cohesive group of tropical trees with a disjunct distribution in Australia, Madagascar, and continental Africa, and diverse flowers associated with two pollination modes. We used custom targeted sequence capture in conjunction with new and existing phylogenetic comparative methods to explore the evolution of floral traits and pollination systems while allowing for reticulate evolution. Our analyses suggest that relationships in Adansonia are confounded by reticulation, with network inference methods supporting at least one reticulation event. The best supported hypothesis involves introgression between A. rubrostipa and core Longitubae, both of which are hawkmoth pollinated with yellow/red flowers, but there is also some support for introgression between the African lineage and Malagasy Brevitubae, which are both mammal-pollinated with white flowers. New comparative methods for phylogenetic networks were developed that allow maximum-likelihood inference of ancestral states and were applied to study the apparent homoplasy in floral biology and pollination mode seen in Adansonia. This analysis supports a role for introgressive hybridization in morphological evolution even in a clade with highly divergent and geographically widespread species. Our new comparative methods for discrete traits on species networks are implemented in the software PhyloNetworks.