The alkali-metal molybdate iodate Na-3(MoO4)(IO3) (I) and mixed-alkali-metal fluoromolybdate Na3Cs(MoO2F4)(2) (II) were obtained via a mild hydrothermal reaction using a "Teflon-pouch" method. I crystallizes in the triclinic space group P (1) over bar, whose structure comprises a 3D backbone made up of isolated [IO3](-) pyramids and [MoO4](2-) tetrahedra connected via 5- and 6-fold coordinated sodium cations. II crystallizes in the monoclinic space group P2(1)/c and comprises isolated [MoO2F4](2-) octahedra with strong out-of-center distortions and the Na+ as well as Cs+ cations acting as interstitial ions. Both compounds have been characterized by infrared (IR) spectra and ultraviolet-visible-near-infrared (UV-vis-NIR) diffuse reflectance spectra. First-principles calculations respectively reveal that they exhibit birefringence values with Delta n = 0.078 and 0.210 at 1064 nm for I and II, and the origin of the birefringence is discussed.