midstream (n.)

"middle; being the middle part or midst; being between, intermediate," Old English mid, midd from Proto-Germanic *medja- (source also of Old Norse miðr, Old Saxon middi, Old Frisian midde, Middle Dutch mydde, Old High German mitti, German mitte, Gothic midjis "mid, middle"), from PIE root *medhyo- "middle."

By late Middle English probably felt as a prefix only, and now surviving in English only as a prefix (mid-air, midstream, etc.). Prefixed to months, seasons, etc. from late Old English. As a preposition, "in the middle of, amid" (c. 1400) it is from in midde or a shortened form of amid (compare midshipman) and sometimes is written 'mid.

Old English stream "a course of water," from Proto-Germanic *strauma- (source also of Old Saxon strom, Old Norse straumr, Danish strøm, Swedish ström, Norwegian straum, Old Frisian stram, Dutch stroom, Old High German stroum, German Strom "current, river"), from PIE root *sreu- "to flow."

From early 12c. as "anything issuing from a source and flowing continuously." Meaning "current in the sea" (as in Gulf Stream) is recorded from late 14c., as is the sense of "steady current in a river." Stream of consciousness in lit crit first recorded 1930, originally in psychology (1855). Stream of thought is from 1890.