mesalliance (n.)

prefix of Germanic origin affixed to nouns and verbs and meaning "bad, wrong," from Old English mis-, from Proto-Germanic *missa- "divergent, astray" (source also of Old Frisian and Old Saxon mis-, Middle Dutch misse-, Old High German missa-, German miß-, Old Norse mis-, Gothic missa-), perhaps literally "in a changed manner," and with a root sense of "difference, change" (compare Gothic misso "mutually"), and thus possibly from PIE *mit-to-, from root *mei- (1) "to change."

Productive as word-forming element in Old English (as in mislæran "to give bad advice, teach amiss"). In 14c.-16c. in a few verbs its sense began to be felt as "unfavorably," and it came to be used as an intensive prefix with words already expressing negative feeling (as in misdoubt). Practically a separate word in Old and early Middle English (and often written as such). Old English also had an adjective (mislic "diverse, unlike, various") and an adverb (mislice "in various directions, wrongly, astray") derived from it, corresponding to German misslich (adj.). It has become confused with mis- (2).

c. 1300, "bond of marriage" (between ruling houses or noble families), from Old French aliance (12c., Modern French alliance) "alliance, bond; marriage, union," from aliier (Modern French allier) "combine, unite" (see ally (v.)).

The general sense of "combination for a common object" is from mid-14c., as are those of "bond or treaty between rulers or nations, contracted by treaty" and "aggregate of persons allied." Unlike its synonyms, "rarely used of a combination for evil" [Century Dictionary]. Meaning "state of being allied or connected" is from 1670s. The Latin word was alligantia.

"marriage with a person of lower social position,"  1738, from mis- (1) "bad, wrong" + alliance. Compare mesalliance.