I noticed something weird just now. I equipped a hero with Narya (10+ vs flying/ring) and got the double hero bonus, when fighting vs flying units. When fighting non flying units, my stack got the ordinary bonus. And then, when there came a flying unit (in the same battle), my units got the +10 and another round of the heroes bonus.
For example: look in game: 12 map: Daradorn Valle
It's LichKing and me.
Battle: second from top, turn 24.