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They are in two separate buildings and departments, but she has already tried to spread rumors to ruin my professional reputation.  Should he alert HR to the situation in case she attempts to do the same with him?

And you.

Hopefully HR will see the wisdom of informing her that discussions about either DH or you are not to be workplace topics.  (And I guess the same would apply to DH henceforth?)

Sadly, I don't know if anything can be done about what she says or does if co-workers go out for a meal or whatever off the job.

Our concern is how much he say without making himself look bad... . does he let them know he is in a high conflict custody battle?  :)oes he let them know about how she spread rumors about me?  It's just sticky because she is soo good at looking like the victim.

Perhaps there are one or two HR professionals on this board that could chime in?  I can't help thinking that if your DH is a successful, respected member of the company than perhaps just staying silent for now is the best way to start.  Let her make the first waves.  People are smart and can figure out that he's been a good guy in the company, she's new, she's his ex-, and she's spouting off due to sour grapes.

If she does start trouble, then a complaint to HR would be in order.

And lots of documentation to take before a judge at your next hearing. 

Regardless, I'd think he'd want to just steer clear and not engage with her at work.

I have an HR background (quickly found that HR Development was a better area than HR Management, because of this very type of thing).

Waddam is right on the money. I would suggest that your DH have a short and succinct conversation with his supervisor, get his/her advice, document the conversation. Emphasize the high conflict nature of the current situation, plus any history of false or exaggerated claims.

If anything further is necessary, the next step is escalating to your HR rep.

Stay calm, professional and out of her way and her business. Hold your head high. Everyone will eventually figure out her angle.

DH told his supervisor, and his supervisor suggested that he document it with HR.  So DH had a 20 minute meeting with HR.  The HR rep seemed very glad that DH brought this to her attention and seemed like she had heard it all before…what DH was telling her was not shocking at all.  He basically told her three things:

1)  That DH and BPD have been in a very contentious custody battle for over three years;

2)  That BPD mom has made some very hurtful allegations about him to friends and family; he said that the allegations are so severe that if they were true, he would be in prison.

and (3) That BPD mom has made some false rumors about me in an attempt to hurt my reputation in my profession as well.