Atypical speech prosody is a hallmark feature of autism spectrum disorder (ASD) that presents across the lifespan, but is difficult to reliably characterize qualitatively. Given the great heterogeneity of symptoms in ASD, an acoustic-based objective measure would be vital for clinical assessment and interventions. In this study, we investigate speech features in child-psychologist conversational samples, including: segmental and suprasegmental pitch dynamics, speech rate, coordination of prosodic attributes, and turn-taking. Data consist of 95 children with ASD as well as 81 controls with non-ASD developmental disorders. We demonstrate significant predictive performance using these features as well as interpret feature correlations of both interlocutors. The most robust finding is that segmental and suprasegmental prosodic variability increases for both participants in interactions with children having higher ASD severity. Recommendations for future research towards a fully-automatic quantitative measure of speech prosody in neurodevelopmental disorders are discussed.