The development of new materials and structures for extreme conditions including impact remains a continuing challenge despite steady advances. Design is currently accomplished using a sequential approach: an optimal material is first developed using the process-structure-properties paradigm, where performance is measured against a blended measure. Then, the structure is optimized while holding the material properties fixed. In this paper, we propose an alternative concurrent and goal-oriented optimization approach where both the material properties and the structure are optimized simultaneously against an overall system-wide performance measure. We develop a non-intrusive, high-performance computational framework based on DAKOTA and GMSH and use it to study the ballistic impact of a double-layer plate of strong AZ31B magnesium alloy and soft polyurea. We show that the proposed concurrent and goal-oriented optimization strategy can provide significant advantage over the traditional sequential optimization approach.