Luminescence properties of CdxZn1-xS/ZnS/MgyZn1-yS separate confinement heterostructures (SCH), CdxZn1-xS/MgyZn1-yS multiple quantum well (MQW) structures, and CdxZn1-xS/ZnS MQW structures grown by low-pressure metalorganic chemical vapor deposition have been studied by mean of temperature-dependent and time-resolved photoluminescence spectroscopy. Biexcitonic luminescence was clearly observed from these structures at 4K. In comparison with the thermal quenching of integrated luminescence intensity observed from CdxZn1-xS/ZnS MQW structure, the thermal quenching observed from CdxZn1-xS/ZnS/MgyZn1-yS SCH structure was suppressed by approximately one order of magnitude. The suppression was attributed to the enhancement of carrier confinement effect by the insert of MgyZn1-yS cladding layer.