MP2 calculations with cc-pVTZ basis set were used to analyze intermolecular interactions in XCCH⋯Y⋯Y, HCCX⋯Y⋯Y, and Y⋯HCCX⋯Y triads (X = Cl, Br; Y = HCN, and HNC) which are connected via hydrogen and halogen bonds. To understand the properties of the systems better, the corresponding dyads are also studied. Molecular geometries, binding energies, and infrared spectra and NMR properties of monomers, dyads, and triads are investigated at the MP2/cc-pVTZ computational level. Particular attention is paid to parameters such as cooperative energies, and many-body interaction energies. Those complexes with simultaneous role of HCCX as hydrogen and halogen donor are diminutive being this energetic effect between 1.09 and 1.42 kJ mol−1. Those complexes with the role of HCCX as hydrogen or halogen donor show cooperativity with energy values ranging between −1.00 and −2.81 kJ mol−1. The electronic properties of the complexes are analyzed using parameters derived from the atoms in molecules (AIM) methodology.