Successful health risk prediction demands accuracy and reliability of the model. Existing predictive models mainly depend on mining electronic health records (EHR) with advanced deep learning techniques to improve model accuracy. However, they all ignore the importance of publicly available online health data, especially socioeconomic status, environmental factors, and detailed demographic information for each location, which are all strong predictive signals and can definitely augment precision medicine. To achieve model reliability, the model needs to provide accurate prediction and uncertainty score of the prediction. However, existing uncertainty estimation approaches often failed in handling high-dimensional data, which are present in multi-sourced data. To fill the gap, we propose UNcertaInTy-based hEalth risk prediction (UNITE) model. Building upon an adaptive multimodal deep kernel and a stochastic variational inference module, UNITE provides accurate disease risk prediction and uncertainty estimation leveraging multi-sourced health data including EHR data, patient demographics, and public health data collected from the web. We evaluate UNITE on real-world disease risk prediction tasks: nonalcoholic fatty liver disease (NASH) and Alzheimer's disease (AD). UNITE achieves up to 0.841 in F1 score for AD detection, up to 0.609 in PR-AUC for NASH detection, and outperforms various state-of-the-art baselines by up to 19% over the best baseline. We also show UNITE can model meaningful uncertainties and can provide evidence-based clinical support by clustering similar patients.