Zanche is a Moorish (North African) maid who works for Flamineo's family. She's carrying on an affair with Flamineo (not an extra-marital affair, though: she's basically his girlfriend), which earns her the scorn of Marcello—who kicks her. Apparently, she and Flamineo are both disinterested in their relationship—Flamineo mocks it, and Zanche quickly abandons him when she sees "Mulinassar"—a Moorish visitor who is really just Francisco de Medici in disguise.
Suddenly, desperately in love with "Mulinassar" (who may have slept with her), she sells out Flamineo—telling "Mulinassar" about how he murdered Camillo and how Brachiano ordered Isabella's death. She wants to elope with "Mulinassar", using some cash she'll rob from Vittoria to help. (5.3). However, this isn't going to happen, given the circumstances. Unfortunately, Gasparo murders her when he and Lodovico break in and get revenge against Flamineo and Vittoria.
Zanche comments poignantly on her fate when she says, earlier, "Alas! poor maids get more lovers than husbands…" (5.1)