Childhood mental health problems are common, impairing, and can become chronic if left untreated. Children are not reliable reporters of their emotional and behavioral health, and caregivers often unintentionally under- or over-report child symptoms, making assessment challenging. Objective physiological and behavioral measures of emotional and behavioral health are emerging. However, these methods typically require specialized equipment and expertise in data and sensor engineering to administer and analyze. To address this challenge, we have developed the ChAMP (Childhood Assessment and Management of digital Phenotypes) System, which includes a mobile application for collecting movement and audio data during a battery of mood induction tasks and an open-source platform for extracting digital biomarkers. As proof of principle, we present ChAMP System data from 101 children 4-8 years old, with and without diagnosed mental health disorders. Machine learning models trained on these data detect the presence of specific disorders with 70-73% balanced accuracy, with similar results to clinical thresholds on established parent-report measures (63-82% balanced accuracy). Features favored in model architectures are described using Shapley Additive Explanations (SHAP). Canonical Correlation Analysis reveals moderate to strong associations between predictors of each disorder and associated symptom severity (r = .51-.83). The open-source ChAMP System provides clinically-relevant digital biomarkers that may later complement parent-report measures of emotional and behavioral health for detecting kids with underlying mental health conditions and lowers the barrier to entry for researchers interested in exploring digital phenotyping of childhood mental health.