First, kudos to you for seeking to support your daughter and her emotions post-divorce. We as adults forget that teens are going through intense hormonal changes, and those hormones start raging about two years before any outward physical changes can be seen. Teenage life is hard these days, so we want to offer all of the support that we can. It's probably difficult for your daughter to understand her parents' need for adult companionship when her parents/family fulfill so many of her social needs at this time.
I think the first step in helping your daughter is for her to understand that you support her father dating. If you lead the way, she will likely follow. It is important for her to understand that it is natural for her father to be interested in developing adult friendships and seeking adult companionship. In fact, this may be your opportunity to introduce the idea that you too may be dating in the future.
One of the most difficult issues for your daughter may be that she feels her father's loyalty will shift as he begins dating. Children often fear that the dating partner will take away from the already diminished time that the child has with the parent. Given that your daughter is a teenager, it is important that she begin a dialogue with her father and let him reassure her that he in no way intends for his dating life to interfere with his relationship with her. While it is good to introduce the dating partner if it as seen as a serious relationship, it should not be that the only interaction the child has with the parent involves his date.
For the most part, it is going to take time. It will take encouragement from both you and your ex-husband to show your daughter that both parents have her interests at heart and are willing to strive for a workable solution. Let her know that you are willing to talk and listen. That, in and of itself, will go a long way.