This woman is obviously an important part of your husband's life. Do you think there might be a way to introduce her to your social circle slowly? Maybe by inviting her to very public events to begin with.
You and your husband know your friends. Is meeting another partner of yours something that is likely to freak them out? I don't know your friends but I think that you're going to have a harder time adjusting to her being around than they are. Chances are your friends will just look upon it as a new person to be friends with.
Maybe you can get better acquainted with her one on one before introducing her to your friends. Once she's more integrated into your life it will seem more natural to invite her to social functions.
Everything will be ok in the end. If it's not ok it's not the end.