The mobile health (mHealth) system, leveraging mobile edge computing, can monitor health status and provide diagnosis. However, due to the privacy of medical data and the resource limitations of mobile devices, patients are unable to access diagnostic services provided by untrusted servers in real-time. Existing schemes present significant challenges in private heterogeneous data aggregation, model training and inference in the presence of malicious participants, and expensive resource consumption. To address these issues, in this paper, we propose a non-interactive privacy-preserving system with the naive Bayesian model, i.e.,$\mathsf {RobustHealth}$, for heterogeneous mHealth diagnosis. Specifically, we extract homogeneous features from heterogeneous datasets to enable efficient encrypted aggregation. We propose a novel private model training algorithm with enhanced security to against collusion-then-differential attacks. We develop a novel non-interactive private model inference algorithm using minimal lightweight cryptographic primitives, designed for patients under unstable network environments. We provide formal security proofs for our system using the Universal Composable (UC) framework. To validate the performance of$\mathsf {RobustHealth}$, we conduct extensive experiments on real-world heterogeneous datasets, and compared with related works. The results demonstrate a$\bf {4.37\%}$improvement in model accuracy, along with significant reductions in computational and communication overheads of$\bf {21.18\times }$and$\bf {4.24\times }$, respectively.