A wood-containing composite are described that may include a lignocellulosic material, and a formaldehyde-free binder in contact with at least a portion of the lignocellulose material. The binder is formed from a binder composition that includes a soy flour, a polymer, and a crosslinking agent, at least a portion of each of which are covalently crosslinked to each other in the binder. Also described are methods of making wood-containing composites by providing a pre-mixed, one-part binder composition of at least 60 wt. % soy flour, a polymer, and a crosslinking agent. The binder composition is applied to lignocellulosic material, and the combination may be heated at a temperature of about 100° C. or more to cure the binder composition into a binder. The cured binder has the soy protein, polymer, and crosslinking agent covalently bonded to each other.