Bitter-sweet is a word, and antithesis is, by definition, a proposition that contradicts a previous one. According to Merriam-Webster, an antithesis is "the rhetorical contrast of ideas by means of parallel arrangements of words, clauses, or sentences (as in "action, not words" or "they promised freedom and provided slavery")."
In literature, we can find plenty of examples of antithesis, such as the famous opening lines in Tolstoi's Anna Karenina: "All happy families are alike; each unhappy family is unhappy in its own way." Or Shakespeare's "Give every man thy ear, but few thy voice." (from Hamlet, act 1, scene 3).
What is bitter-sweet, then? A two-word paradox known as an oxymoron, as already stated and explained by other educators. This answer is valid from a linguistic perspective, although a cook would probably tell you that this word is used to describe a unique flavor, and not necessarily a contradictory mix between something bitter and something sweet.