We propose to use lattice-matched AlInN/GaN to replace the Al(Ga)N/GaN material system for III-nitride Bragg reflectors, despite the poor material quality of AlInN reported until very recently. We report an improvement of AlInN material that allowed for successful fabrication of a microcavity light emitting diode, a distributed Bragg reflector with 99.4% reflectivity and microcavities with a quality factor over 800. These results establish state-of-the-art values for III-nitrides, and announce the future importance of AlInN in GaN-based optoelectronics.