A new class of metal-nonmetal-metal sandwich structures M-3-CO3-M-3' (M, M' = Li, Na, K) with all real frequencies is obtained at the second-order Moller-Plesset theory (MP2) method with the 6-311 +G (2d) basis set. Because the sandwich molecule M-3-CO3-M-3' is composed of superatoms (M-3, CO3, and M-3'), it is a sandwich "superomolecule". The superatoms M-3 are electron donors and CO3 is the acceptor, and then there is a strong charge transfer between M-3 (or M-3') and CO3 superatom, so M-3-CO3-M-3' can be denoted as M3+CO32-M3'(+). Owing to the CO32- anion in the middle repulsing the valence electrons of two metal rings (M-3 and M-3') forming a pair of excess electrons, the compound with excess electrons is also a novel electride. In metal-nonmetal-metal sandwich compound M3+CO32-M3'(+), superatom units M-3(+) and M-3'(+) exhibit unusual sigma-aromaticity: the maximum negative nucleus-independent chemical shift (NICSmax) value of each aromatic ring (M-3(+) or M-3('+)) does not locate at the center of the ring plane but locates outside the ring plane. The distance value from the center of the M-3(+) or M-3'(+) ring plane to the point with NICSmax ranges from 0.8 to 1.9 angstrom. This shows a notable out-of-plane sigma-aromaticity for these sandwich compounds. What is the reason? We find that the out-of-plane sigma-aromaticity of M-3(+) (or M-3'(+)) results from the action of CO32-M3'(+) (or M3+CO32-). For electric property, on account of excess electrons, the sandwich electride M-3-CO3-M-3' without the central symmetry can exhibit large static first hyperpolarizability (beta(0)). For Na-3-CO3-K-3, the beta(0) value is close to 56 000 au.