First of all, I think you are really brave for coming onto a forum and baring your heart and your emotions, strong as though they may be for others to comment. That's pretty cool, and that's honesty.
I have to say that I agree with Redpepper that DADT generally causes more harm than good. It seems from what I've observed, that DADT relationships are put in place because someone isn't willing to put in the work for a truly open honest communicative relationship. I personally feel that DADT relationships can be at best limiting, and at worst dangerous.
Do you know for sure if this person is using protection with his partners? You don't know who he is sleeping with, and could be opening yourself up to STDs or other diseases.
That being said, I also agree with redpepper that getting to know your partner's other partner might be helpful to you, and may be the tool you need to help you conquer your fear. I know that you are new to all of this, so realize that when you are new you are going to need to take steps that might seem scary or uncomfortable at first. That's how we gain the experience that brings wisdom and happy poly lives.
An example from my own life is that my boyfriend's wife is almost like a sister to me because she and I can share things that nobody else can; we can collaborate together to do nice things for him, and for each other. We can support each other when the other has a problem, and we can be friends! If I had been afraid to talk to her, I would be missing out on the beautiful connection and love that we share. Just remember, this lady may have been reaching out to you because she wants to be your friend!
I wish you the best of luck. I would not have chosen your situation for myself because I prefer more open and honest communicative types of relationships; but I've been poly for a long time, and I'm not you, I don't know what's attracted you to this man; and I cannot judge why other people pursue relationships and attractions. I do hope that all works out well for you.
I suggest that you read up on the definitions of poly, go to some local meetups, and talk to others with strong poly relationships. To me, your boyfriend seems like he wants to have his cake and eat it too more than really be poly; but again, I don't know the situation for sure, so I can't truly say.