In existing modular adaptive control approaches, the effects of external disturbances such as atmospheric turbulence are often not considered. In real-life flight applications, stochastic atmospheric disturbances can severely degrade the performance of these approaches, resulting in undesired and unpredictable control behavior. In this paper, robust adaptation laws are developed within the framework of multivariate-spline-based adaptive control. This new approach, referred to as robust spline-based adaptive nonlinear dynamic inversion (R-SANDI), integrates nonlinear dynamic inversion (NDI) and spline-model-based control allocation with a robust real-time aerodynamic model identification routine. The latter is based on the conditional estimation of the deterministic and the disturbance effect. The developed method is applied to control a F-16 aircraft subject to significant aerodynamic uncertainties and turbulence. Simulation results show that the developed control system outperforms a previously proposed deterministic spline-based adaptive NDI controller, which is shown to become unstable in the presence of turbulence. The new controller is able to adapt to large uncertainties within the onboard aerodynamic model, even in the co-existence of high turbulence levels. This enhances flight performance, safety and survivability and facilitates future real-life flight applications in high performance aircraft.