Alzheimer’s disease (AD) is a progressive, neurodegenerative disorder mainly characterized by memory loss with deficits in other cognitive domains, including language, visuospatial abilities, and changes in behavior. Detecting diagnostic biomarkers that are noninvasive and cost-effective is of great value not only for clinical assessments and diagnostics but also for research purposes. Several previous studies have investigated AD diagnosis via the acoustic, lexical, syntactic, and semantic aspects of speech and language. Other studies include approaches from conversation analysis that look at more interactional aspects, showing that disfluencies such as fillers and repairs, and purely nonverbal features such as inter-speaker silence, can be key features of AD conversations. These kinds of features, if useful for diagnosis, may have many advantages: They are simple to extract and relatively language-, topic-, and task-independent. This study aims to quantify the role and contribution of these features of interaction structure in predicting whether a dialogue participant has AD. We used a subset of the Carolinas Conversation Collection dataset of patients with AD at moderate stage within the age range 60–89 and similar-aged non-AD patients with other health conditions. Our feature analysis comprised two sets: disfluency features, including indicators such as self-repairs and fillers, and interactional features, including overlaps, turn-taking behavior, and distributions of different types of silence both within patient speech and between patient and interviewer speech. Statistical analysis showed significant differences between AD and non-AD groups for several disfluency features (edit terms, verbatim repeats, and substitutions) and interactional features (lapses, gaps, attributable silences, turn switches per minute, standardized phonation time, and turn length). For the classification of AD patient conversations vs. non-AD patient conversations, we achieved 83% accuracy with disfluency features, 83% accuracy with interactional features, and an overall accuracy of 90% when combining both feature sets using support vector machine classifiers. The discriminative power of these features, perhaps combined with more conventional linguistic features, therefore shows potential for integration into noninvasive clinical assessments for AD at advanced stages.