From Ancient Greekἐπιφύτον(epiphúton, “one [plant] that grows upon another plant”), from ἐπί(epí, “on top of”) + φυτόν(phutón, “plant”), via epi-(“above, over”) +-phyte(“plant”).
1848, John Lindley, A notice of some species of Rhododendron inhabiting Borneo: Journal of the Royal Horticultural Society, volume 3, page 88:
It has been suggested to me that these fine plants will not prove cultivable, because they are epiphytes.[…]The probability however is, that they do not require to be treated as epiphytes, and that, like orchids, they will grow better if committed judiciously to the earth.
1893, Natural Science: A Monthly Review of Scientific Progress, volume 3, page 185:
The nature of the surface of a plant also determines the number and sort of Epiphytes which lodge on it.