Interfacial binding and phonon mismatch are two crucial parameters in determining thermal boundary conductance. However, it is difficult for polymer/metal interfaces to possess both significant interfacial binding and weak phonon mismatch to achieve enhanced thermal boundary conductance. Herein, we circumvent this inherent trade-off by synthesizing a polyurethane and thioctic acid (PU-TA) copolymer with multiple hydrogen bonds and dynamic disulfide bonds. Using PU-TA/aluminum (Al) as a model interface, we demonstrate that the thermal boundary conductance of the PU-TA/Al interfaces measured by transient thermoreflectance is 2-5 times higher than that of traditional polymer/Al interfaces, which is attributed to the highly matched and bonded interface. Furthermore, a correlation analysis is developed, which demonstrates that interfacial binding has a greater impact than phonon mismatch on thermal boundary conductance at a highly matched interface. This work provides a systematic understanding of the relative contributions of the two dominant mechanisms to thermal boundary conductance by tailoring the polymer structure, which has applications in thermal management materials.