By correlating all electrons and employing core-tuned correlation consistent basis sets of quintuple-zeta quality, we applied multireference and coupled-cluster methods to study 32 electronic states of the diatomic BH molecule, two bound states of BH(-), and three states of the linear HBBH molecule. We have constructed full potential energy curves and profiles, reporting binding energies, geometries, spectroscopic parameters, dipole moments, and energy separations, whereas our numerical results are in excellent agreement with available experimental numbers. We are trying as well to interpret the binding modes of a large number of the examined states. 18 states of BH are of Rydberg character, with the BH(-) anion revealing similar structural characteristics to the isoelectronic CH species. The first three states of HBBH X 3Sigma g (-), a 1Delta g, and b 1Sigma g + diabatically correlate to two a 3Pi BH fragments, they are similar to the states b 3Sigma g (-), B 1Delta g, and B' 1Sigma g + of the isoelectronic molecule C2, however, their ordering follows that of the first three states of the O2 molecule.