In home health care (HHC) services, nurses or professional caregivers are dispatched to patients’ homes to provide medical care services, such that each patient can stay at home to be treated periodically. The HHC problem consists of the nurse rostering problem (NRP) and the vehicle routing problem with time windows (VRPTW), both of which are NP-hard problems, which are harder or equal to the hardest problem in the NP (nondeterministic polynomial time) problem class and generally cannot be solved efficiently. To the best of our knowledge, the previous algorithmic approaches were designed to separately address NRP and VRPTW of the HHC problem. However, NRP and VRPTW of the HHC problem are intercorrelated, and their respective optimal objectives may be in conflict with each other in many cases. Additionally, the problem generally involves too many constraints to be solved, and most previous works did not address occurrence of sudden incidents in HHC services (e.g., a nurse or a patient suddenly requests for a leave, and a patient suddenly changes the time slot to be treated) such that the original nurse roster could become infeasible. Under constraints of nurse qualifications, working laws, nurse preferences, and vehicle routing, the first model considers nurse rostering and vehicle routing concurrently to minimize total costs of nurse overtime and vehicle routing. The second model extends the first model with rerostering caused by occurrence of sudden incidents. Harmony search algorithm (HSA) has been shown to perform better in solving NRPs than conventional metaheuristics, and hence this work proposes an improved HSA with genetic and saturation schemes, in which the solution representation is designed to concurrently determine nurse rostering and vehicle routing. For the second rerostering model, inheritance and immigrant schemes are added to the HSA to adapt to the change caused by occurrence of sudden incidents. Experimental results show that the proposed HSA performs well and can adapt to the change caused by sudden incidents.