The electronic structure of a series of double layer (Sr3V2O7, KLaNb2O7, Li2SrNb2O7, RbLaNb2O7, Rb2LaNb2O7) as well as triple layer (Ca4Ti3O10, K2La2Ti3O10, Sr4V3O9.7, CsCa2Nb3O10) Dion-Jacobson and Ruddlesclen-Popper phases and quadruple layer A(n)B(n)O(3n+2) phases (Sr2Nb2O7 as well as the low-temperature and room-temperature structures of Sr2Ta2O7) has been studied by means of a first-principles density functional theory approach. The results are rationalized on the basis of a simple tight-binding scheme, which provides a simple yet precise scheme allowing the correlation of the crystal structure details and the nature of the bottom t(2g)-block band levels. Both the quantitative and the qualitative approaches are used to analyze the nature of the carriers in intercalated samples of the d(0) semiconducting phases as well as those of the metallic d(x) (0 < x <= 1) systems. The Ruddlesden-Popper and Dion-Jacobson materials with partially filled t(2g)-block bands must be genuine two-dimensional metals except when the M-O-ap distances of the outer layer octahedra are similar and the band filling is not low. The conducting electrons in these phases are almost equally distributed among the different layers. It is shown that the A(n)B(n)O(3n+2) phases with partially filled bands are potentially interesting materials because they are structurally two-dimensional materials exhibiting one-dimensional band structure features. Finally, the possible application of the simple scheme to related materials such as layered perovskite oxynitrides and the effect of disorder are briefly discussed.