A QoS multicast routing scheme based on Genetic Algorithms (GA) heuristic is presented in this paper. Our proposal, called Constrained Cost–Bandwidth–Delay Genetic Algorithm (CCBD-GA), is applied to a multilayer hybrid platform that includes High Altitude Platforms (HAPs) and a Satellite platform. This GA scheme has been compared with another GA well-known in the literature called Multi-Objective Genetic Algorithm (MOGA) in order to show the proposed algorithm goodness. In order to test the efficiency of GA schemes on a multicast routing protocol, these GA schemes are inserted into an enhanced version of the Core-Based Tree (CBT) protocol with QoS support. CBT and GA schemes are tested in a multilayer hybrid HAP and Satellite architecture and interesting results have been discovered. The joint bandwidth–delay metrics can be very useful in hybrid platforms such as that considered, because it is possible to take advantage of the single characteristics of the Satellite and HAP segments. The HAP segment offers low propagation delay permitting QoS constraints based on maximum end-to-end delay to be met. The Satellite segment, instead, offers high bandwidth capacity with higher propagation delay. The joint bandwidth–delay metric permits the balancing of the traffic load respecting both QoS constraints. Simulation results have been evaluated in terms of HAP and Satellite utilization, bandwidth, end-to-end delay, fitness function and cost of the GA schemes.