The first Ga(0.5)ln(0.49)P/GaAs inverted-structure high electron mobility transistors (I-HEMT) and insulated-gate inverted-structure high electron mobility transistors (I2HEMT) grown by gas source molecular beam epitaxy (GSMBE) have been fabricated and measured. Very high drain-to-source breakdown voltage was obtained in the I-HEMT (23 V) and I(2)HEMT (13 V). The maximum g(m)s achieved for I-HEMT and I(2)HEMT were 120 and 100 mS/mm at room temperature, respectively. No I-V collapse was observed at 77 K. The high breakdown characteristics were attributed to the use of a high band gap GaInP passivation layer between the gate and drain. These results indicate that Ga0.51I0.49P/GaAs I-HEMT and I(2)HEMT are promising to be used as high breakdown (high power) devices.