This paper reports a detailed study of InAs-InAsx Sb-1-x Type-II superlattice (SL) midwave infrared laser structures, in which the band-to-band radiative transitions are spatially indirect, from extended electron states in the conduction band to relatively localized heavy-hole states in the valence band. Due to the large valence band offset between InSb and InAs, the effective bandgap of InAs-InAsxSb1-x Type-II SL can cover a broad infrared wavelength range, from 3.0 mu m to far infrared (> 10 mu m). Under CW optical pumping, stimulated light emission is observed from laser structures consisting of InAs-InAsxSb1-x Type-II SL active regions capped by AlAs0.16Sb0.84 cladding layers. The operating wavelengths are around 3.4 mu m, which is in good agreement with theoretical modeling. The overlap between electron and hole wavefunctions along the growth direction is calculated to be 0.89. Equivalent CW threshold current densities are 3.3 A/cm(2) and 56 A/cm(2) at sample temperatures of 5 K and 95 K, respectively, The corresponding characteristic temperature (T-o) is 32 K. These results demonstrate that the InAs-InAsxSb1-x Type-II SL is a very promising candidate material for midwave infrared semiconductor lasers.