The ability to create architected materials that possess both high stiffness and toughness remains an elusive goal, since these properties are often mutually exclusive. Natural materials, such as bone, overcome such limitations by combining different toughening mechanisms across multiple length scales. Here, a new method for creating architected lattices composed of core–shell struts that are both stiff and tough is reported. Specifically, these lattices contain orthotropic struts with flexible epoxy core–brittle epoxy shell motifs in the absence and presence of an elastomeric silicone interfacial layer, which are fabricated by a multicore–shell, 3D printing technique. It is found that architected lattices produced with a flexible core‐elastomeric interface‐brittle shell motif exhibit both high stiffness and toughness.