We demonstrate the generation of broadband dispersive waves (DWs) and solitons in an 80-cm tellurite microstructured optical fiber (TMOF) designed and fabricated with 78TeO2-5ZnO-12LiCO3-5Bi2O3 (TZLB) glass. A 1810-nm femtosecond laser is used as the pump source with an average pump power ranging from 33 mW to 175 mW, where the tunable frequency range is 211.1 THz, which corresponds to the tunable wavelength range of 1742.9 nm. At 175 mW, the trapped multiple DWs are located at 923.8 nm, 1039.2 nm, 1121.6 nm, and 1204.6 nm and the multiple solitons are located at 2666.7 nm, 2426.1 nm, 2165.9 nm, 1952.7 nm, and 1842.1 nm. The experimentally obtained maximum DW conversion efficiency is 14%, and the maximum soliton conversion efficiency is 43%. The experimental and theoretical results of pulse evolution in the TMOF agree very well. To the best of our knowledge, this is the first time that nine peaks of frequency conversions have been realized simultaneously in non-silicon fibers. The exceptionally high nonlinearity and broadband-tunable characteristics of the proposed TMOF are promising components for the development of compact and highly efficient tunable mid-infrared fiber lasers, wavelength converters, and time-frequency metrology.