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.

The word "bittersweet" is not an example of antithesis; however, it is a great example of oxymoron.  An oxymoron is a figure of speech that combines contrasting terms for effect.  So, because the separate terms "bitter" and "sweet" contrast each other, their combination creates an oxymoron. 

An example of antithesis is seen in the following line from Mark Twain's essay "The Lowest Animal":  "The cat is innocent, Man is not."  An antithesis is a rhetorical device in which parallel structure is used to juxtapose two contrasting ideas.  The line from Twain's essay juxtaposes the innocence of cats with the innocence of humans to suggest that the cat naturally has this character trait, while man/woman does not.  Writers use antithesis to highlight claims and statements through contrast.