This work reports an implementation of a novel realization of the multireference coupled cluster theory formulated in Fock space. Extending the previous formulation carried out in the (1,1) [M. Musial, R. J. Bartlett, J. Chem. Phys. 129, 044101 (2008)], (0,2) [M. Musial, R. J. Bartlett, J. Chem. Phys. 135, 044121 (2011)], and (2,0) [M. Musial, J. Chem. Phys. 136, 134111 (2012)] sectors to the (3,0) sector, we are able to treat structures with three valence electrons. The (3,0) sector describes systems with three electrons added to the reference, which means that in order to perform correlated calculations for the neutral AB molecule, we have to adopt as the reference a triply ionized structure AB 3+. A desirable situation occurs when such an ion has a closed-shell structure and also dissociates into closed shell fragments. This feature makes it possible to apply the restricted Hartree-Fock scheme for the whole range of interatomic distances. Examples of molecules of this type are the diatomics formed by the atoms of alkali metals and alkaline earth metals. An analogous structure is also exhibited by alkali metal monocarbides. In the current work, we have calculated the potential energy curves and spectroscopic constants for the LiBe, LiC, and NaC molecules.