Composite [two or more different materials] bows have been around for a long time; wood, bamboo, horn, baleen, sinew, etc.
In the context of my question, two or more "materials," one being man made or produced by processing various natural polymers. The modern composite bow developed during the 1940s, laminated, generally of at least three laminations.
A fiberglas backed, maple cored, plastic faced bow would be a typical, modern composite from the late 1940s.