He is in love with another!

Hi April & Forum Readers!
I have been in an open relationship with my boyfriend of 5 months. We started out together with the open relationship having talked out our preliminary terms from the start. He was in a non-monogamous relationship for five years before being with me whereas I had just come out of a 7 year monogamous relationship. This is something I had been looking for as I had been unhappy with the terms of my former relationship. Now, in my current situation, we agreed to be each others primary partner, emotionally exclusive, but NOT sexually exclusive. We agreed to build boundaries or set rules as we go and learn more about each others needs. He is adamant about being dependable and committed to me, wanting me to trust him and feel secure. However, there is already an issue. He is in love with an other girl.
He has known this girl for several years. She is younger than he is, and she lost her virginity to him. He met her during the course of his previous relationship and it was an issue for them. He is not having sex with her, but he sees her at least a couple times a month. He has explained to me that they are not together because they want different things. She wants monogamy, marriage, children, a house, the whole nine and he does not. I, too, do not want those normal things which is one of the ways we match well together. Before he pursued me they talked it out and decided that it would not work out between them because of these fundamental differences, which seems logical.
After a recent visit with her, he informed me that she broke up with her boyfriend upon which I expressed my concern that she may be holding out for him. He became immediately defensive at this and immediately denied this as a possibility claiming that she is far to clear headed for that, that I do not know her, and he should know as he has known her for years that this would not be in her character. Yet, they both are openly in love with each other. He has told me he will not leave me for her. Another concern of mine is that he says he tries to encourage her to break out of her shell. I told him that to me it sounded like he is encouraging her to become a person he could be with. He denies this as well saying that if she actually changed, she would not be the same girl he loves and he would be angry with her. My feeling is that he wishes she would become this changed woman he could be with and the only reason he claims he would no longer love her is because he is not ready to risk a true love monogamous commitment.
I have expressed all of my feelings and concerns to him and he says that he will do anything to help me feel more secure, except stop seeing her. Their love was pre-existing, can not be denied and is an exception to our emotionally exclusive terms. I can not help but feel terrible pain every time her name is mentioned, when I know they will see each other, or even at the thought of them seeing each other. There more in love I fall with him, the more difficult this becomes. We have not come up with any solution for this problem. I do not want him to keep his meetings with her from me in order to avoid making me miserable and having it ruin an entire day together. I told him I don’t want this because I value the honesty in our relationship and I feel like it would be unfair for him to be protected from the pain I am in because of this.
I am still quietly suffering from this. What in the world can I do. Leaving him is not a consideration, however I worry about how this will affect our future or if he will ever love me the same. I am desperate for suggestions on how to cope and my friends are unable to offer advice since none of them understand non-monogamy.