We investigate the possibility of realizing unconventional superconductivity in doped band insulators on the square and honeycomb lattices. The latter lattice is found to be a good candidate due to the disconnectivity of the Fermi surface. We propose applying the theory to the superconductivity in doped layered nitride β-MNCl (M= Hf, Zr). Finally, we compare two groups of superconductors with disconnected Fermi surface, β-MNCl and the iron pnictides, which have high critical temperature Tc, despite some faults against superconductivity are present.