Significant enhancement in green emission by integrating a thin AlInN barrier layer, or interlayer (IL), in an InGaN/GaN multiple quantum well (MQW) is demonstrated. The MQWs investigated here contains 5 periods of an InGaN QW, a 1 nm thick AlInN IL, and a 10 nm thick GaN barrier grown by metalorganic chemical vapor deposition. To accommodate the optimum low-pressure (20 Torr) growth of the AlInN layer a growth flow sequence with changing pressure is devised. The AlInN IL MQWs are compared to InGaN/AlGaN/GaN MQWs (AlGaN IL MQWs) and conventional InGaN/GaN MQWs. The AlInN IL MQWs provide benefits that are similar to AlGaN ILs, by aiding in the formation of abrupt heterointerfaces as indicated by X-ray diffraction omega-2theta (x-2h) scans, and also efficiency improvements due to high temperature annealing schedules during barrier growth. Room temperature photoluminescence of the MQW with AlInN ILs shows similar performance to MQWs with AlGaN ILs, and $4-7 times larger radiative efficiency (pump intensity dependent) at green wavelengths than conventional InGaN/GaN MQWs. This study shows the InGaN-based MQWs with AlInN ILs are capable of achieving superior performance to conventional InGaN MQWs emitting at green wavelengths.