It is a great challenge to develop polymeric materials possessing multiple functionalities for their intrinsic properties. In our efforts to overcome this dilemma, we report a carbon nanotube (CNT)-doped polymer architecture design in this paper using a soft matrix synthesized from methacrylic acid and poly(ethylene glycol) methacrylate via reversible addition–fragmentation chain-transfer polymerization and further functionalized by 1-pyrenemethanol and doped with hard, stiff CNTs as fillers. The CNTs were dispersed evenly into the pyrene-functionalized copolymers obtained via the solution blending method. Our approach is simple, low-energy-consuming, facile in operation, and highly efficient. The developed composites demonstrate high mechanical strength, self-healing ability, and high electrical conductivity. To further maximize the potential of our CNT-filled composites, we introduced a simple but effective means to align CNTs by directional stretching at elevated temperatures and so achieved significant mechanical and electrical reinforcement. The multifunctional composites produced in this paper have desirable properties for future applications such as conductive bioskins, healthcare monitoring sensors, and other functional conductive electronics.