The quality of healthcare services is influenced by the maturity of healthcare processes used to develop it. A maturity model is an instrument to assess and continually improve organizational processes. In the last decade, a number of maturity models have been proposed with varied focus and depth for business processes. However, the number of studies that adapt these models to healthcare domain or propose healthcare-specific maturity models is very scarce. In this study, we share our experience and observations on assessing the healthcare processes of a hospital department in accordance to a well-known Business Process Maturity Model (BPMM) by Object Management Group (OMG). We also discuss challenges of assessing maturity of healthcare processes in accordance to a generic maturity model and outline opportunities for future work.