Optimized structures, with all real frequencies, of superalkali superhalides (Li(3))(+)(SH)(-) (SH=LiF(2), BeF(3), and BF(4)), are obtained, for the first time, at the B3LYP/aug-cc-pVDZ and MP2/aug-cc-pVDZ computational levels. These superalkali superhalides possess three characteristics that are significantly different from normal alkali halides. 1) They have a variety of structures, which come from five bonding mode types: edge-face, edge-edge, face-face, face-edge, and staggered face-edge. We find that the bonding mode type closely correlates with the Li(3)-SH bond energy. 2) The valence electrons on the Li(3) ring are pushed out by the (SH)(-) anion, and become excess electrons, conferring alkalide or electride characteristics on these Li(3)-SH species, depending on the bonding mode type. 3) The highest occupied molecular orbital of each Li(3)-SH species is a doubly occupied delocalized sigma bonding orbital on the Li(3) ring, which indicates its aromaticity. It is noticeable that the maximum negative nucleus-independent chemical shift value (about -10 ppm) moves out from the center of the Li(3) ring, owing to repulsion by the SH(-) anion. We find that these superalkali superhalides are not only complicated "supermolecules", but are also a new type of alkalide or electride, with aromaticity.