We demonstrate the design, production, characterization and application of two dispersive complementary mirror pairs compensating second- and third-order dispersion, respectively. Both mirror pairs operate in the spectral range from 1.2-3.2µm. This is an unprecedented bandwidth of over 1.4 octaves which can drive further improvements in Cr:ZnS, Cr:ZnSe and other laser systems with a central wavelength around 2µm. The first pair provides a constant group delay dispersion of -100fs2, while the second one enables the compensation of the third-order dispersion that is introduced by a TiO2 crystal.