Cocrystal monohydrate of nitrofurantoin (NF) with melamine (MELA) has been studied as NF is an antibacterial drug used for the treatment of urinary tract infections. The structure of nitrofurantoin-melamine-monohydrate (NF-MELA-HO) is characterized by FT-IR and FT-Raman spectroscopy. The energies and vibrational frequencies of the optimized structures calculated using quantum chemical calculations. Supported by normal coordinate analyses and potential energy distributions (PEDs), the complete vibrational assignments recommended for the observed fundamentals of cocrystal hydrate. With the aim of inclusion of all the H-bond interactions, dimer of NF-MELA-HO has been studied as only two molecules of cocrystal hydrate are present in the unit cell. By the study of dimeric model consistent assignment of the FT-IR and FT-Raman spectrum obtained. H-bonds are of essential importance in an extensive range of molecular sciences. The vibrational analyses depict existence of H-bonding (O-H⋯N) between water O-H and pyridyl N atom of MELA in both monomer and dimer. To probe the strength and nature of H-bonding in monomer and dimer, topological parameters such as electron density (ρ), Laplacian of electron density (∇ρ), total electron energy density (H) and H-bond energy (E) at bond critical points (BCP) are evaluated by quantum theory of atoms in molecules (QTAIM). Natural bond orbitals (NBOs) analyses are carried out to study especially the intra and intermolecular H-bonding and their second order stabilization energy (E). The value of HOMO-LUMO energy band gap for NF-MELA-HO (monomer and dimer both) is less than NF, showing more chemical reactivity for NF-MELA-HO. Chemical reactivity has been described with the assistance of electronic descriptors. Global electrophilicity index (ω = 7.3992 eV) shows that NF-MELA-HO behaves as a strong electrophile than NF. The local reactivity descriptors analyses such as Fukui functions, local softnesses and electrophilicity indices performed to determine the reactive sites within NF-MELA-HO. In MEP map of NF-MELA (monomer and dimer) electronegative regions are about NO and C=O group of NF, although the electropositive regions are around NH, N-H group and HO molecule. Molar refractivity (MR) value of NF-MELA-HO (monomer and dimer) lies within the range set by Lipinski's modified rules. This study could set as an example to study the H-bond interactions in pharmaceutical cocrystals.