This is an unpleasant passive aggressive person.

What I've tried:

1. Waiting this person out. The problem with this, is the person I'm thinking of will start lying (or implying untrue things about me) in such a way that gives others (who overhear or listen in) a BAD wrong impression if you don't interject.

2. Making my point concisely and loudly. The problem with that is she still will not acknowledge what I said. Instead, she will start acting as if I'm angry and saying things to imply that.

What else can I do?

Edit: It has occurred to me that maybe she's trying either get me to do something that she can complain about or to "crock something up" to complain about.