The reflectance spectra of the superionic glasses uCuI .(1 - x)Cu2MoO4 (x = 0.4, 0.5) have been measured in the mid- and far-infrared range to investigate the structure of the oxyanion matrix and the nature of sites hosting the charge carrier copper ions. The analysis of the mid-infrared spectra revealed the presence of three types of molybdate polyhedra : MoO42- monomers (the majority units), Mo2O72- dimers (minority units), and MoO66- isolated octahedra (minority units). The presence of MoO4/2O22- type octahedra, which contain four bridging and two nonbridging oxygen atoms, was excluded on the basis of the spectroscopic results. The relative abundance of the three types of molybdate structural units was found to depend on the glass transition temperature, T-g; the equilibrium between those molybdate units shifts toward dimers and octahedra upon decreasing T-g. This is effected by increasing the mole fraction of CuI in the glass. Thus, CuI affects indirectly the glass structure by lowering the temperature at which the structure of the supercooled liquid is frozen into the glassy state. The study of the far-infrared profiles has suggested that the cuprous ions exist in three coordination environments; two of these are formed by oxygen atoms provided by the oxyanion matrix and the third is formed primarily by iodide anions. The vibrational characteristics of such CuI-like environments suggest their disordered nature with respect to crystalline CuI. The findings of this work are in agreement with the results of our previous investigations on analogous AgI-containing glasses and lends support to the conduction pathway model proposed for ion transport in such superionic glasses. Calculation of effective charges on the basis of the far-infrared data indicated that copper is present in the +1 oxidation state in these glasses.