THAAD, I think, can intercept targets on re-entry, so it would work that Japanese and ROK radar would pick up the launch and calculate its ballistic arc, if that arc lands within Japanese or ROK territory then the order to open fire will be given. If the missile is still in its boost phase (going up) then I believe that AEGIS warships will be able to intercept with their RIM-161 missiles which can hit objects in Low Earth Orbit (including satellites) which will explode near the missile, shredding the outside which will cause an explosion as the volatile fuel mixture ignites.
THAAD uses a more direct method in that its missile just basically rams the target at high speed, that would probably go after the warhead if it has separated from the missile, although given the relatively small distances involved in a strike on the ROK or Japan, the AEGIS system could probably intercept at the warhead too.
The future will likely bring railguns and lasers to the fore in Anti-Ballistic Missile technology, railguns being able to fire projectiles at ridiculous speeds at or in front of launching missiles, and lasers to melt the missile or warheads skin to the point that it burns up or explodes.
Of course, you load up the ROK and Japan with enough ABM tech to completely defeat the DPRK threat then the PRC is going to get a bit antsy since it also has beef with the ROK and Japan and such defence systems would also annull the Chinese missile advantage.
