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The carrier aircraft's accurate control plays a fundamental and vital role during the air recovery of swarm unmanned aerial vehicles. To handle the control problem of the air recovery carrier with trajectory and posture constraints under unknown complex airflow disturbances, this paper proposes a robust constrained flight controller by integrating the integral Barrier Lyapunov function (iBLF) based dynamic surface control (DSC) method with the high-order sliding mode disturbance observer. Firstly, the carrier's six DOF affine nonlinear dynamics considering the unknown airflow disturbances are established for controller design convenience. Secondly, several finite-time convergent super-twisting sliding mode observers are designed to accurately observe the "lumped disturbances" in each subsystem composed of the airflow effect and other unmeasured items. Then, by taking these estimated disturbances as a kind of feed-forward compensating signals, an iBLF-based DSC is established for the carrier's constrained flight required by the specific air recovery mission. Moreover, closed-loop stability is analyzed. Finally, the flight simulations are performed to show the constrained control performance and the anti-disturbance ability of the proposed carrier flight controller, even under unknown airflow disturbances. [ABSTRACT FROM AUTHOR]