Various layered boronitrides (LaN)(n)(TM2B2) (T-M = transition metal; n = 2, 3) have been prepared using a high-pressure synthesis technique in which an inverse alpha-PbO-type TM2B2 layer is separated by two or three rock salt-type LaN layers and these layers are connected through linear (BN) units. The electronic states of the distinguishing (BN) unit and intermediate rock salt-type LaN layer are discussed on the basis of density functional theory calculations. Bulk superconductivity has been found in LaNiBN (T-c approximate to 4.1 K), CaNiBN (T-c approximate to 2.2 K), and LaPtBN (T-c approximate to 6.7 K), where the Fermi level E-F is located in the bands composed of the T-M(d)-B(2p) antibonding state and the main T-M(d) band resides well below E. The non-superconductive T-M-based compounds exhibit Pauli paramagnetic behavior, in which the highly itinerant nature of the electrons caused by strong T-M(d)-B(2p) covalent bonding suppresses the long-range magnetic ordering.