Systematic　three-dimensional　finite　element　(FE)　simulations　are　carried　out　to　study　the　ballistic　protection　performance　of　double-layer　sandwich　plates　having　metallic　pyramidal　lattice　truss　cores　filled　with　ceramic　prism　insertions　and　void-filling　epoxy　resin.　Both　normal　and　oblique　projectile　impacts　are　considered　in　the　FE　simulations　that　are　validated　against　experimental　measurements.　The　ballistic　limit　velocity,　the　energy　absorbed　by　key　constituting　elements　and　the　critical　oblique　angle　corresponding　to　the　transition　from　ballistic　perforation　to　projectile　embedment　are　calculated.　As　the　oblique　angle　is　increased,　the　evolution　of　deformation　and　failure　in　the　double-layer　plates　as　well　as　the　underlying　mechanisms　are　explored.　It　is　demonstrated　that　the　proposed　double-layer　sandwich　plates　outperform　both　the　single-layer　sandwich　plates　and　the　homogeneous　(monolithic)　metallic　plates　having　equal　total　mass,　and　the　top　layer　(the　ceramic　insertions　in　particular)　of　the　double-layer　configuration　plays　a　more　dominant　role　in　energy　absorption.