Yes, but spitting in someone's face, on it's own, regardless of whether there's a complaint or not, isn't necessarily assault. Without accompanying violence or the threat of violence, it's battery (unlawful application of force upon a person). Therefore it can't be assault with a weapon, or aggravated assault, as it fails the "assault" part.
He says he loses his rag. The incident occurs over several minutes. And then he spits at her. I'd say there is a threat of violence.