In electronic health records, many biomarkers of different types are measured irregularly for each subject. It is important but challenging to integrate these temporal biomarkers for disease prognosis and personalized treatment. In this work, we develop a unified framework to simultaneously model different types of temporal processes (e.g., rates of adverse events, continuous laboratory tests, binary incidence of comorbidities) and their measurement intensity through multi-level, generalized exponential family distributions with latent processes. We characterize the temporal network-dependencies among these processes and account for potentially informative patterns in healthcare practices such as laboratory test times. Using these methods, we are able to extract latent and dynamic dependency structures from these biomarkers so as to quantify between-subject similarity. Finally, we demonstrate our methods through simulation studies and application to EHR data for type 2 diabetic patients.