It seems to me you feel the word "affair" is disrespectful to D, because you love her fully, completely. But I feel you are the one who started disrespecting your relationship with her when you hid it. While it was hidden, it was an affair, and it was limited because how much can you do when you have to hide it?
Now that it's open, it stops being an affair, and starts being a fuller relationship (once again, if you all work at it). I can see you really love D and don't want to use a word that you feels diminishes the relationship you guys have... But the relationship was diminished by the lies, and the word reflects that accurately. That's how I feel about it at least.