This paper proposes a novel orientation-aware model predictive control (MPC) for dynamic humanoid walking that can plan footstep locations online. Instead of a point-mass model, this work uses the augmented single rigid body model (aSRBM) to enable the MPC to leverage orientation dynamics and stepping strategy within a unified optimization framework. With the footstep location as part of the decision variables in the aSRBM, the MPC can reason about stepping within the kinematic constraints. A task-space controller (TSC) tracks the body pose and swing leg references output from the MPC, while exploiting the full-order dynamics of the humanoid. The proposed control framework is suitable for real-time applications since both MPC and TSC are formulated as quadratic programs. Simulation investigations show that the orientation-aware MPC-based framework is more robust against external torque disturbance compared to state-of-the-art controllers using the point mass model, especially when the torso undergoes large angular excursion. The same control framework can also enable the MIT Humanoid to overcome uneven terrains, such as traversing a wave field.