This note addresses an open control problem: control of sandwich nonsmooth nonlinear systems. Of interest are sandwiched nonsmooth nonlinearities between linear dynamic blocks, as illustrated by a hydraulic valve system with a sandwiched dead-zone. A hybrid control scheme for control of such sandwich systems is developed and presented in detail in this note. The proposed control scheme employs an inner-loop discrete-time feedback design and an outer-loop continuous-time feedback design, combined with a nonlinearity inverse, to cancel the nonlinearity effect, for improving output tracking. Stability and tracking performance of the closed-loop control system are analyzed. Simulations are used to illustrate the effectiveness of the proposed hybrid control design.