We report for the first time on molecular beam epitaxial growth of new hybrid Al(Ga)Sb/InAs/Cd(Mg)Se heterostructures and studies of their structural, luminescence and transport properties. The structures demonstrate intense photoluminescence (PL) in both visible and infra-red spectral regions. The results of luminescence and structural measurements indicate the rather high structural quality of the A(3)B(5)/A(2)B(6) interface. Theoretical estimations of band line-ups in these structures predict type II band alignment for the InAs/CdSr interface, which transforms to type I with increasing the Mg content in a CdMgSe alloy. A valence band offset as large as 1.6eV is expected at the InAs/Cd(Mg)Se interface. The results of electron transport measurements along the interface are in good agreement with the theoretical estimation.