The F3YLi…NCH…HMH and F3YLi…HMH…HCN triads (Y=C, Si; M=Be, and Mg) are connected by lithium and dihydrogen bonds. To understand the properties of the systems better, the corresponding dyads are also studied. Molecular geometries, binding energies, infrared spectra and NMR properties of monomers, dyads, and triads are investigated at the MP2/6-311++G** computational level. Particular attention is paid to parameters, such as cooperative energies, and many-body interaction energies. Triads with the HMH molecule located at the end of the chain, show energetic cooperativity ranging between −3.66 to −7.59 kJ mol-1. When the HMH molecule is located in the middle, the obtained cluster is diminutive with an energetic effect between 3.49 to 5.17 kJ mol-1. The electronic properties of the complexes are analyzed using parameters derived from the atoms in molecules (AIM) methodology.