This article presents a whole-body controller for humanoid robots affected by concentrated link flexibility. We characterize the link flexibility by introducing passive joints at the concentration of deflections, which separate the flexible links into two or more rigid bodies. In this way, we extend our robot model to take link deflections into account as underactuated extra degrees of freedom, allowing us to design a whole-body controller capable to anticipate deformations. Since in a real scenario, the deflection is not directly measurable, we present an observer aiming at estimating the flexible joint state, namely position, velocity, and torque, only considering the measured contact force and the state of actuated joint. We validate the overall approach in simulations with the humanoid robot TALOS, whose hip is mechanically flexible due to a localized mechanical weakness. Furthermore, the paper compares the proposed wholebody control strategy with state-of-the-art approaches. Finally, we analyze the performance of the estimator in the case of different values of hip elasticity.