Chop the sweet and unsweetened chocolates into small chunks. Place in a bowl set over simmering water and melt together. Set aside, but keep warm.
Whip the heavy cream until soft peaks form. Reserve.
Whip the egg yolks, eggs, and sugar for about 3 minutes at high speed; the mixture should be light and fluffy. Bring the honey to a boil and gradually pour it into the egg mixture while whipping. Continue whipping until cold.
Fold in the reserved chocolate and the chartreuse. Quickly stir in the whipped cream.