Inserts having geometrically separate materials for slips on downhole tool

A downhole tool, such as a fracture plug used during a fracture operation, installs in a downhole tubular, such as casing. The tool has a mandrel with a sealing element disposed thereon between uphole and downhole ends. Slip assemblies on the mandrel can be moved to engage the downhole tubular. When the tool is used as a bridge plug, the uphole assembly supports the sealing element compressed, and the downhole assembly supports fluid pressure downhole of the tool. The slip assemblies have inserts composed of at least two materials that are different from one another and are geometrically separate from one another. In addition or as an alternative, the slip assemblies can be composed of at least two different materials that are geometrically separate from one another.