There are emerging transportation problems known as the Traveling Salesman Problem with Drone (TSPD) and the Flying Sidekick Traveling Salesman Problem (FSTSP) that involve using a drone in conjunction with a truck for package delivery. This study presents a hybrid genetic algorithm for solving TSPD and FSTSP by incorporating local search and dynamic programming. Similar algorithms exist in the literature. Our algorithm, however, considers more sophisticated chromosomes and less computationally complex dynamic programming to enable broader exploration by the genetic algorithm and efficient exploitation through dynamic programming and local search. The key contribution of this paper is the discovery of how decision-making processes for solving TSPD and FSTSP should be divided among the layers of genetic algorithm, dynamic programming, and local search. In particular, our genetic algorithm generates the truck and the drone sequences separately and encodes them in a type-aware chromosome, wherein each customer is assigned to either the truck or the drone. We apply local search to each chromosome, which is decoded by dynamic programming for fitness evaluation. Our new algorithm is shown to outperform existing algorithms on most benchmark instances in both quality and time. Our algorithms found the new best solutions for 538 TSPD instances out of 920 and 74 FSTSP instances out of 132.