Does it count as a divorce if the husband says to his wife, "Divorce me," and she replies, "You are divorced," when this was done as a joke and without the intention of divorce?

This كناية (allusive statement) is not considered a divorce unless it was intended as an authorization for the wife (to divorce herself), and she, by her words, intended divorce. As long as you did not intend divorce or authorization, and she did not intend for it to occur, then no divorce takes place, and your wife remains under your marital bond. Nevertheless, one must be cautious with such words, for divorce, whether serious or in jest, is equally binding.