I wouldn't bother mentioning this to your friend.
I have read some of your other posts and respect that would are uncomfortable with someone referring to you as "the woman." This is perfectly acceptable as each person has their own style and preferences.
However, your friend probably does not have this issue. She does not find this behaviour unacceptable. She probably either finds it tolerable or even endearing.
If you bring this up with your friend, you risk testing your friendship. The man is not dating you, he is dating her. If he uses a word or phrase when speaking or texting YOU, you can say "I really don't like being referred to as "___," It's just a personal quirk. I would prefer you just use my name." Say this with a smile or a . As for his communication style with others - let the others tell him what they prefer. It's just not really your business otherwise.
Notwithstanding everything I said above - if your friend mentions that she is being hurt (physically or emotionally), you might encourage her to seek outside help if she feels it necessary (e.g. through a women's center). However, these cases are pretty extreme. Calling someone "my woman" is not emotional/physical abuse.
BTW - I am referred to as "the Mrs" by my husband. We have been happily married for 7 years.