Yes, the male is genetically a YH bird.
http://www.finchinfo.com/genetics/lady_ ... colors.php
"If two yellow head genes are present on a bird that has no red head genes (and instead has black head genes), the bird will have a black head with a yellow tipped beak (YTB). This occurs because the bird is genetically a yellow headed bird, but it cannot express the yellow color because the yellow gene depends on the red head gene for expression, and the red head gene is not there."
With a BH hen all the chicks will be BH/YH (BlackHead split to YellowHead) because the chick would need 2 YH genes to be a YH and only the male would have a YH gene to pass on. BH/YH have red tipped beaks.
If your hen is split to YH then the chicks would either be a BH/YH or BH YTB (BlackHead YellowTippedBeak) because they could get a YH gene from each parent making them genetically YH.
Hope that explained it well without confusing you more.