We demonstrate that mercury and antimony compounds with chalcogens (Q = S, Se, Te) and halogens (X = I, Cl, Br) can be a promising family for radiation detection materials. Chalcogen p-orbitals are usually located near the Fermi level and they are responsible for relative high mobilities but at the same time band gap decreases (from S to Te) due to their extended interactions. Halogens on the other hand have their bands well below the Fermi level and salts between transition metals and halogen are usually insulators. Incorporation of halogen atoms in a mercury or antimony chalcogenide framework can give rise to intermediate properties between the two end members (HgQ and HgX2), i.e. structures composed of heavy elements (Z > 40), wide band gap (1.6 - 2.5 eV), and high carrier mobilities. As a proof of concept, we will present two new chalcohalide families, Hg3Q2X2 and SbQX. Crystal growth of the Hg3Te2Br2 phase (7.8 g/cm3 and 2.5 eV) by a vapor transport method gave mm-sized single crystals with electrical resistivity values more in the GΩ.cm range. Preliminary data for mobility-lifetime products for both electron and hole carriers were around 10-5 cm2/V. SbSeI (5.8 g/cm3 and 1.7 eV) sample grown by relatively fast Bridgman technique showed an MΩ.cm range (2.8 × 106 Ω.cm) resistivity with a similar order of magnitude (10-4 cm2/V) of mobility-lifetime products for both electron and hole carriers.