Optimization studies of dynamic systems using high-fidelity numerical models necessitate a tradeoff between fidelity and the total computational time required during design. A gradient-based optimization framework is proposed for the aerodynamic shape and controller design of aerodynamic systems using computationally intensive high-fidelity models. Subject to some general properties, the framework offers flexibility in the types of simulation models used and provides guarantees regarding closeness to an optimal design. A nested optimization loop that allows for the partitioning of controller and plant architecture is implemented. The proposed framework exploits time-scale properties of the dynamic system model, closeness properties of partially converged iterative solutions of computational fluid dynamics models, and the continuous adjoint method. It is shown that combining these methods can improve the total computational time relative to finite differencing. An example of optimizing the aerodynamic body and control gains of a tail-fin controlled supersonic missile is presented.