Hybrid electric aircraft (HEA), as a promising concept in sustainable aviation, will play a critical role in mitigating the climate impacts of the aviation sector. While many companies have taken up the goal of designing and manufacturing HEA in the near future, there is a technical gap in how to evaluate the operational implementation of HEA within existing airline networks. Significant challenges involve seamlessly integrating HEA into existing airline schedules, ensuring that they are adequately charged for each mission, and strategically assigning HEA with consideration to their range constraints and fuel burn savings. In this study, we address barriers to airline operations of HEA by developing realistic operating cost estimations for HEA, together with a mathematical fleet assignment optimization model to demonstrate practical HEA usage for regional airlines seeking to incorporate these new aircraft into their fleets. We demonstrate our fleet assignment model with a realistic regional airline network, comparing pre-HEA and post-HEA adoption optimal fleet assignments. Our modeling efforts enable the evaluation of the potential for HEA to be integrated into commercial airline fleets, and the potential for cost savings as well as environmental benefits.