Currently, liquid metal (LM)-based multifunctional soft composites are an emerging class of materials with transformative potential towards flexible electronics, soft robotics, and reconfigurable functionality. Herein, we report an innovative soft bi-phasic composite system by exploiting the H-bonding interaction of LMs with a chemically modified styrenic block copolymer chain, resulting in a soft and ultrastretchable elastomeric material architecture with excellent multifunctional properties. The influence of microstructure and interfacial interactions on the multifunctional properties has been established and also validated using various mathematical models such as Eshelby’s approach, modified Cole–Cole model, and effective medium theory to understand the origin of the unique properties of such materials. The resulting composites exhibit a significant fourfold improvement in the dielectric permittivity and more than 350% improvement in thermal conductivity over neat polymer while maintaining deformability with more than 1400% strain at break. This work provides a cost-effective, facile, and scalable approach to the construction of soft multifunctional composites for soft matter engineering applications.