Single-walled carbon nanotubes (SWNTs) are recognized as the ultimate carbon fibers for high-performance, multifunctional composites. The remarkable multifunctional properties of pristine SWNTs have proven, however, difficult to harness simultaneously in polymer composites, a problem that arises largely because of the smooth surface of the carbon nanotubes (i.e., sidewalls), which is incompatible with most solvents and polymers, and leads to a poor dispersion of SWNTs in polymer matrices, and weak SWNT-polymer adhesion. Although covalently functionalized carbon nanotubes are excellent reinforcements for mechanically strong composites, they are usually less attractive fillers for multifunctional composites, because the covalent functionalization of nanotube sidewalls can considerably alter, or even destroy, the nanotubes' desirable intrinsic properties. We report for the first time that the molecular engineering of the interface between non-covalently functionalized SWNTs and the surrounding polymer matrix is crucial for achieving the dramatic and simultaneous enhancement in mechanical and electrical properties of SWNT-polymer composites. We demonstrate that the molecularly designed interface of SWNT-matrix polymer leads to multifunctional SWNT-polymer composite films stronger than pure aluminum, but with only half the density of aluminum, while concurrently providing electroconductivity and room-temperature solution processability.