Ballistic resistant armor material and assembly including a thin, rigid armor component for stopping and capturing ballistic projectiles, backed by a resilient component formed of thermoplastic elastomeric honeycomb material for absorbing projectile strike energy and reducing impact noise and/or blunt trauma injury. The armor component includes multiple layers of high tensile strength aramid fabric or the like sandwiched between front and back plates made of multiple layers of woven carbon cloth impregnated with an epoxy resin or the like. The several layers of the armor component are formed and compressed to provide a rigid outer shell that can advantageously be configured as planar or shaped to suit particular applications. The resilient component is affixed to the inside surface of the armor component and may include one or more layers of flexible honeycomb material having cells that are open, hermetically sealed, or perforated to provide fluid circulation therethrough.