ACuIn(PO4)2 compounds (A = K and Rb) have been prepared by the flux method and solid-state reaction. They were characterized by X-ray diffraction (XRD), Scanning Electron Microscopy (SEM) with Energy Dispersive X-Ray analysis (EDX), Fourier Transform Infra-Red (FTIR), Raman and optical spectroscopies, as well as a Density Functional Theory (DFT) study has been performed. Single XRD analysis shows that the compounds were isostructural and crystallize in the monoclinic centrosymmetric P21/n space group. There are one A (Na, K or Rb), one Cu, one In, two P and eight O sites in the asymmetric unit of the ACuIn(PO4)2 structure. Its structure is made up from corners-sharing between InO6 octahedra and Cu2O8 units, built up from edge-sharing of two CuO5 polyhedra, to form zigzag chains ranging infinitely along the b axis. The inter-connection between these chains is assured by the PO4 tetrahedra creating a 3D framework with six-sided tunnels parallel to the  direction, where the A+ ions are located. XRD diagrams of the powder samples reveal the formation of single purity phases with monoclinic symmetry. FTIR and Raman spectroscopies revealed the presence of two isolated PO4 groups in the analyzed phosphates. The SEM-EDX verifies the morphology and the chemical composition of the synthesized samples. The diffuse reflectance spectroscopy (DRS) has proven an indirect bandgap of 3.34 eV, 3.33 and 2.82 eV for NaCuIn(PO4)2, KCuIn(PO4)2 and RbCuIn(PO4)2, respectively. The electronic bandgap structure and bonding character analysis of important atom pairs in the ACuIn(PO4)2 structure are also studied in details.