Morphological characters are indispensable in phylogenetic analyses for understanding the pattern, process, and tempo of evolution. If characters are independent and free of systematic errors, then combining as many different kinds of characters as are available will result in the best-supported phylogenetic hypotheses. But since morphological characters are subject to natural selection for function and arise from the expression of developmental pathways, they may not be independent, a situation that may amplify any underlying homoplasy. Here, we use new dental and multi-locus genetic data from bats (Mammalia: Chiroptera) to quantify saturation and similarity in morphological characters and introduce two likelihood-based approaches to identify strongly conflicting characters and integrate morphological and molecular data. We implement these methods to analyze the phylogeny of incomplete Miocene fossils in the radiation of Phyllostomidae (New World Leaf-nosed Bats), perhaps the most ecologically diverse family of living mammals. Morphological characters produced trees incongruent with molecular phylogenies, were saturated, and showed rates of change higher than most molecular substitution rates. Dental characters encoded variation similar to that in other morphological characters, while molecular characters encoded highly dissimilar variation in comparison. Saturation and high rates of change indicate randomization of phylogenetic signal in the morphological data, and extensive similarity suggests characters are non-independent and errors are amplified. To integrate the morphological data into tree building while accounting for homoplasy, we used statistical molecular scaffolds and combined phylogenetic analyses excluding a small subset of strongly conflicting dental characters. The phylogenies revealed the Miocene nectar-feeding †Palynephyllum nests within the crown nectar-feeding South American subfamily Lonchophyllinae, while the Miocene genus †Notonycteris is sister to the extant carnivorous Vampyrum. These relationships imply new calibration points for timing of radiation of the ecologically diverse Phyllostomidae.