The Air-breathing Hypersonic Vehicle (AHV) is characterized by high nonlinearity, strong coupling, and inherent uncertainties. To ensure the safe operation of the Scramjet, a stringent constraint on the Angle of Attack (AoA) is imperative. We introduce an innovative three-channel coupled control approach for the AHV that incorporates the AoA constraint. An Incremental Nonlinear Dynamic Inversion (INDI) controller is formulated to address model uncertainty, while the non-minimum phase challenge is mitigated through output redefinition and poles placement. Additionally, an Exponential Control Barrier Function (ECBF) tailored for the AoA constraint is developed and integrated with the INDI within a Quadratic Programming (QP) framework, termed INDI-CBF-QP. Simulation results demonstrate that our proposed method not only tracks longitudinal load and roll angle commands swiftly and stably but also achieves a reduced angle of sideslip compared to traditional, decoupled designs. Moreover, it maintains the critical AoA constraint even in the presence of significant model parameter uncertainty.