Psychiatrists diagnose mental disorders via the linguistic use of patients. Still, due to data privacy, existing passive mental health monitoring systems use alternative features such as activity, app usage, and location via mobile devices. We propose FedTherapist, a mobile mental health monitoring system that utilizes continuous speech and keyboard input in a privacy-preserving way via federated learning. We explore multiple model designs by comparing their performance and overhead for FedTherapist to overcome the complex nature of on-device language model training on smartphones. We further propose a Context-Aware Language Learning (CALL) methodology to effectively utilize smartphones' large and noisy text for mental health signal sensing. Our IRB-approved evaluation of the prediction of self-reported depression, stress, anxiety, and mood from 46 participants shows higher accuracy of FedTherapist compared with the performance with non-language features, achieving 0.15 AUROC improvement and 8.21% MAE reduction.