In this study, a novel biobased poly(ethylene brassylate)-poly(furfuryl glycidyl ether) copolymer (PEBF) copolymer was synthesized and applied as a structure-directing template to incorporate graphene and 1,1′-(methylenedi-4,1-phenylene)bismaleimide (BMI) to fabricate a series of self-healing organic/inorganic hybrid materials. This ternary material system provided different types of diene/dienophile pairs from the furan/maleimide, graphene/furan, and graphene/maleimide combinations to build a crosslinked network via multiple Diels–Alder (DA) reactions and synergistically co-assembled graphene sheets into the polymeric matrix with a uniform dispersibility. The PEBF/graphene/BMI hybrid system possessed an efficient self-repairability for healing structural defects and an electromagnetic interference shielding ability in the Ku-band frequency range. We believe that the development of the biobased self-healing hybrid system provides a promising direction for the creation of a new class of materials with the advantages of environmental friendliness as well as durability, and shows potential for use in advanced electromagnetic applications.