Business process analysis and process mining, particularly within the health care domain, remain under-utilized. Applied research that employs such techniques to routinely collected health care data enables stakeholders to empirically investigate care as it is delivered by different health providers. However, cross-organizational mining and the comparative analysis of processes present a set of unique challenges in terms of ensuring population and activity comparability, visualizing the mined models, and interpreting the results. Without addressing these issues, health providers will find it difficult to use process mining insights, and the potential benefits of evidence-based process improvement within health will remain unrealized. In this article, we present a brief introduction on the nature of health care processes, a review of process mining in health literature, and a case study conducted to explore and learn how health care data and cross-organizational comparisons with process-mining techniques may be approached. The case study applies process-mining techniques to administrative and clinical data for patients who present with chest pain symptoms at one of four public hospitals in South Australia. We demonstrate an approach that provides detailed insights into clinical (quality of patient health) and fiscal (hospital budget) pressures in the delivery of health care. We conclude by discussing the key lessons learned from our experience in conducting business process analysis and process mining based on the data from four different hospitals.