High nonlinearity and transparency in the 1–5 μm spectral range make tellurite glass fibers highly interesting for the development of nonlinear optical devices. For nonlinear optical fibers, group velocity dispersion that can be controlled by microstructuring is also of great importance. In this work, we present a comprehensive numerical analysis of dispersion and nonlinear properties of microstructured two-, four-, six-, and eight-core tellurite glass fibers for in-phase and out-of-phase supermodes and compare them with the results for one-core fibers in the near- and mid-infrared ranges. Out-of-phase supermodes in tellurite multicore fibers are studied for the first time, to the best of our knowledge. The dispersion curves for in-phase and out-of-phase supermodes are shifted from the dispersion curve for one-core fiber in opposite directions; the effect is stronger for large coupling between the fields in individual cores. The zero dispersion wavelengths of in-phase and out-of-phase supermodes shift to opposite sides with respect to the zero-dispersion wavelength of a one-core fiber. For out-of-phase supermodes, the dispersion can be anomalous even at 1.55 μm, corresponding to the operating wavelength of Er-doped fiber lasers.