A systematic ab initio investigation has been carried out to determine the structures, binding energies, and spin-spin coupling constants of ternary complexes X:CNH:Z and corresponding binary complexes X:CNH and CNH:Z, for X, Z = CNH, FH, ClH, FCl, and HLi. The enhanced binding energies of ternary complexes X:CNH:Z for fixed X as a function of Z decrease in the same order as the binding energies of the binary complexes CNH:Z. In contrast, the enhanced binding energies of the ternary complexes for fixed Z as a function of X do not decrease in the same order as the binding energies of the binary complexes X:CNH, a consequence of the increased stabilities of ternary complexes FCl:CNH:Z due to very strong chlorine-shared halogen bonds. For complexes in which the X···CNH interaction is a D-H···C hydrogen bond for D-H the proton-donor group (N-H, F-H, or Cl-H), spin-spin coupling constants (1)J(D-H) and (2h)J(D-C) in ternary complexes X:CNH:Z decrease in absolute value as the binding energies of binary complexes CNH:Z and the enhanced binding energies of the ternary complexes for fixed X as a function of Z also decrease. However, (2X)J(F-C) increases as the enhanced binding energies of the ternary complexes FCl:CNH:Z decrease, a consequence of the nature of the chlorine-shared halogen bond. The one-bond coupling constants (1)J(N-H) for the CNH···Z interaction in ternary complexes vary significantly, depending on the nature of the X···CNH interaction. The largest values of (1)J(N-H) are found for ternary complexes with FCl as X. Two-bond coupling constants (2h)J(N-A) for A the proton-acceptor atom of Z, and (2d)J(N-H) decrease in absolute value in the order of decreasing enhancement energies of ternary complexes X:CNH:Z for fixed Z as a function of X.