The chemical treatment of carbon fibers used in carbon fiber-epoxy matrix composites greatly affects the fraction of hydrogen bonds (H-bonds) formed at the fiber-matrix interface. The H-bonds are major contributors to the fiber-matrix interfacial shear strength and play a direct role in the interlaminar shear strength (ILSS) of the composite. The H-bond contributions τ to the ILSS and magnitudes KN of the fiber-matrix interfacial stiffness moduli of seven carbon fiber-epoxy matrix composites, subjected to different fiber surface treatments, are calculated from the Morse potential for the interactions of hydroxyl and carboxyl acid groups formed on the carbon fiber surfaces with epoxy receptors. The τ calculations range from 7.7 MPa to 18.4 MPa in magnitude, depending on fiber treatment. The KN calculations fall in the range (2.01 – 4.67) ×1017 N m−3. The average ratio KN/|τ| is calculated to be (2.59 ± 0.043) × 1010 m−1 for the seven composites, suggesting a nearly linear connection between ILSS and H-bonding at the fiber-matrix interfaces. The linear connection indicates that τ may be assessable nondestructively from measurements of KN via a technique such as angle beam ultrasonic spectroscopy.