This numerical study is dedicated to investigating the ballistic performance of three-component integral body armor comprising ceramic façade, layers of ultra-high molecular weight polyethylene fiber-based composite (Dyneema) and closed-cell aluminum foam against NIJ-Type IV armor-piercing bullets. A numerical model of integral armor with a ceramic façade and a fiber-reinforced composite backing plate was developed in IMPETUS Afea Solver and verified against experimental data. The verified model was used to design a "baseline configuration" of two-component integral armor that can stop the NIJ-Type IV projectiles. Three-component armor configurations were obtained by introducing layer(s) of closed-cell aluminum foam into the laminate. Laminates with different stacking sequences of composite and porous layers and different foam relative densities were studied and compared with the baseline two-component configuration. The study presents new insights into the mechanics of perforation of integral armor with closed-cell foam and provides design recommendations for such armor systems.