@Rozzak Kufa projects himself and his dead mother upon Melida. He wants her to have the life he (and his mother) never had, loved and respected by everyone while holding her head up with dignity and pride. This complements her dream. Kufa has basically made Melida the cornerstone for his own happiness.
The entire assassination job is based on Melida being confirmed (or at least widely perceived) to be proof of her mother's infidelity. So far, the Duke isn't buying into the rumors that she isn't his child, only that the gossip itself is threatening his place in society. Kufa thus sees a chance to bargain for more time to stamp out the chatter and prove her worth as an Angel. The game's not done yet.
Of course, his attachment is also clearly developing into romantic affection, so it's becoming harder and harder to imagine him ultimately defaulting to killing her and wiping the slate clean. He is in too deep.