Melissa appears in several episodes of Two and a Half Men during Season 6.
Melissa was first introduced as a character in season 6, episode 4, The Flavin and the Mavin.
Her role in the show, like all women besides Berta and the Harper brother’s mother, is to be a love interest. She is first the romantic partner of Charlie for a weekend and later in season 6 she dates Alan.
While Melissa was one of my favorite characters in the show, she really had no depth and the role was tiny… It’s kind of sad really.