The epoxy/amine nucleophilic ring-opening reaction of furfurylamine (FA) with diglycidyl ether of bisphenol A (DGEBA) at a molar ratio of 1/1 generated a polyaddition oligomer (FADGEBA). Mixtures of FADGEBA, 4,4-bismaleimidodiphenylmethane (BMI), and melamine (ML) at FADGEBA(as a repeating unit)/BMI/ ML molar ratios of 2/4/1, 4/5/1, 6/6/1, and 2/1/0 were prepolymerized at 110 °C and hot-pressed at 110-130 °C to produce cured products (FADGBA-BMI-ML-241, -451, -661, and -210). Fourier transform infrared (FT-IR) spectroscopy revealed the occurrence of the maleimide/amine Michael addition of BMI/ML and the furan/ maleimide Diels-Alder (DA) reaction of FADGEBA/BMI. The onset temperatures of the endothermal retro DA reaction for FADGBA-BMI-MLs were ~ 150 °C. The 5% mass loss temperature of FADGEBA-BMI-ML-241 at 347 °C was significantly higher than those of the other cured products. The flexural strengths and flexural strains at break of FADGBA-BMI-MLs increased in the order of FADGEBA-BMI-ML-241 < FADGEBA-BMI-ML-451 < FADGEBA-BMI-ML-661 < FADGEBA-BMI-ML-210, whereas the flexural moduli decreased in the same order. All cured products showed healing properties when hot-pressed at 160 °C/5 MPa. The healing efficiencies on flexural strength were 57-82%.