The impact resistance of layered polymer structures using polyvinyl butyral (PVB) in combination with Kevlar® fabric and ultra-high molecular weight polyethylene (UHMWPE) were fabricated and tested. Methods of wet impregnation and hot-press impregnation and consolidation of fabric with PVB and UHMWPE were used to manufacture multilayer constructs. All sandwich constructs were fixed to the surface of ballistic clay and subject to a free drop-weight test with a conical impactor having a small contact area. All tests were made at the same impact energy of 9.3 J and velocity of 2.85 m/s. The change in the resistance force was recorded using a piezoelectric force sensor at the time intervals of 40 μs. Using experimental force–time history, the change in the impactor’s velocity, the depth of impactor penetration, the energy transformation at various stages of impactor interaction with the sample, and other parameters were obtained. Three indicators were considered as the main criteria for the effectiveness of a sample’s resistance to impact: (1) minimum deformation, bulging, of the panel backside at the moment of impact, (2) minimum absorption of impact energy per areal density, and (3) minimal or, better yet, no destruction of structural integrity. Under the tested conditions, the rigid Kevlar–PVB–Kevlar sandwich at the frontside and relatively soft but flexible UHMWPE–Kevlar–UHMWPE layers in the middle helped to localize and absorb impact energy, while the backside Kevlar–PVB–Kevlar sandwich minimized local bulging providing the best overall performance. The front layer damage area was very shallow and less than two impactor tip diameters. The backside bulging was also less than in any other tested configurations.