Hearing is multifaceted, and the relative contributions of peripheral and central hearing loss are rarely considered together in the context of dementia. Here, we assessed peripheral (as measured with pure-tone audiometry) and central (as measured with dichotic listening) hearing in 19 patients with typical amnestic Alzheimer's disease (tAD), 10 patients with logopenic variant primary progressive aphasia (lvPPA), 11 patients with nonfluent/agrammatic variant PPA (nfvPPA), 15 patients with semantic variant PPA (svPPA), and 28 healthy age-matched individuals. Participants also underwent neuropsychological assessment and magnetic resonance image scanning, allowing us to use voxel-based morphometry to assess associations between hearing scores and grey matter volume. Dichotic listening was impaired in all patient groups relative to healthy controls. In the combined patient (but not healthy control) cohort, dichotic listening scores were significantly correlated with measures of global cognitive functioning and speech-based neuropsychological tasks. Pure-tone audiometry scores were not significantly elevated in any patient group relative to the healthy control group, and no significant correlations were observed between peripheral hearing and neuropsychological task performance in either the combined patient or healthy control cohorts. Neuroanatomically, dichotic listening performance was associated with grey matter volume in a bilateral fronto-temporoparietal network over the combined patient cohort, but no correlates were identified for pure-tone audiometry. Our findings highlight the importance of speech parsing mechanisms beyond elementary sound detection in driving cognitive test performance, underline the importance of assessing central hearing alongside peripheral hearing in people with dementia, and further delineate the complex auditory profiles of neurodegenerative dementias.