The orthorhombic $MgB_2C_2$ structure contains well-separated parallel graphite-like $B_2C_2^{2-}$ layers which extend infinitely in two dimensions. Three possible ways to distribute B and C atoms in the hexagonal sublattice sites are adopted. Band structures for the hypothetical distribution patterns are examined to assess the electronic stability of these phases and to account for the observed arrangement by means of extended Huckel tight-binding calculations. The preferred choice is the layer with B and C alternating strictly so that B is nearest neighbor to C and vice versa. A rationale for this is given. Due to the alternation of B and C within the honeycomb layers, $MgB_2C_2$ is a band insulator, which through partial substitution of Mg with Li, is predicted to turn metallic with holes in the $sigma$ bands at the Fermi level.