midwife: [14] A midwife is etymologically a ‘with-woman’. The mid- element represents the long extinct preposition mid ‘with’ (its Germanic relatives are still alive and well: German mit, Dutch met, and Swedish and Danish med). Wife preserves the original meaning of Old English wīf, ‘woman’. The idea underlying the word is that a midwife is ‘with’ a woman giving birth. [midwife etymology, midwife origin, 英语词源]
c. 1300, "woman assisting," literally "woman who is 'with' " (the mother at birth), from Middle English mid "with" (see mid) + wif "woman" (see wife). Cognate with German Beifrau.