In this paper, by introducing the software-defined networking (SDN) controller, we conduct traffic scheduling under dual connectivity (DC) pattern to support handover management in the heterogeneous aeronautical network. First, we construct a stochastic optimization problem of handover overhead with queue backlog, under the condition of ensuring user fairness and limited resource constraints. Then, we utilize the Lyapunov optimization theory to transform the stochastic optimization problem into a deterministic optimization problem and propose feasible and optimal strategies. Finally, we verify the feasibility and effectiveness of those strategies on handover management by simulations in two different aeronautical scenarios.