We performed accurate ab initio investigations of the geometric parameters and the vibrational structure of neutral HNS/HSN triatomics and their singly charged anions and cations. We used standard and explicitly correlated coupled cluster approaches in connection with large basis sets. At the highest levels of description, we show that results nicely approach those obtained at the complete basis set limit. Moreover, we generated the three-dimensional potential energy surfaces (3D PESs) for these molecular entities at the coupled cluster level with singles and doubles and a perturbative treatment of triple excitations, along with a basis set of augmented quintuple-zeta quality (aug-cc-pV5Z). A full set of spectroscopic constants are deduced from these potentials by applying perturbation theory. In addition, these 3D PESs are incorporated into variational treatment of the nuclear motions. The pattern of the lowest vibrational levels and corresponding wavefunctions, up to around 4000 cm(-1) above the corresponding potential energy minimum, is presented for the first time.