[Khammet]

5 I think
level 4 did not have it, level 8 did have it

[Discordian]

I'm pretty sure they give it to you early before level 10 because a ninja can use H2H.

[Onorgul]

Ninja only get Dual Wield at level 10 and while they can use H2H, they don't necessarily. I would imagine that it would be a level 10 or 15 ability for Ninja.

As for Monk, I have no idea (being level 35), but I can only imagine that level 5 as Khammet stated is about right.

[loial]

My 10 Mnk had it, my 10 SAM/MNK had it, but my 9 BLM/MNK did not.

Monks do indeed get it at 5.

[Onorgul]

Yay for research! I suppose I could have pulled out my 11 White Mage to check it, but it didn't occur to me. Still wondering when Ninja get it, though.