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We present detailed design of a highly nonlinear chalcogenide core tellurite cladding composite microstructured fiber and dispersion tailoring in it. The fabrication procedure for the microstructured fiber is explained. Its applications to nonlinear phenomena are described with the experimental demonstration of the supercontinuum generation and the simulation of the parametric gain. It is observed that a supercontinuum spectrum of 20 dB bandwidth covering 0.80-2.40 μm is generated by this composite microstructure fiber when 1.85 μm pump is used. The simulation results show that the bandwidth over which the calculated parametric gain is more than 10 dB is 1680 nm, ranging from 1.04 to 2.72 μm.