We report free space visible light communication using InGaN sources, namely micro-LEDs and a laser diode, down-converted by a red-emitting AlInGaP multi-quantum-well nanomembrane. In the case of micro-LEDs, the AlInGaP nanomembrane is capillary-bonded between the sapphire window of a micro-LED array and a hemispherical sapphire lens to provide an integrated optical source. The sapphire lens improves the extraction efficiency of the color-converted light. For the case of the down-converted laser diode, one side of the nanomembrane is bonded to a sapphire lens and the other side optionally onto a dielectric mirror; this nanomembrane-lens structure is remotely excited by the laser diode. Data transmission up to 870 Mb/s using pulse amplitude modulation (PAM) with fractionally spaced decision feedback equalizer is demonstrated for the micro-LED-integrated nanomembrane. A data rate of 1.2 Gb/s is achieved using orthogonal frequency division multiplexing (ODFM) with the laser diode pumped sample.