Bismark
I presume this means that the JHF and JHC will deploy under command of the Joint Commander surely?
Another jump to far.
JHC and JHF are peacetime organizations. They do not fight as entities.
Harriers can deploy under the JFACC or JMCC and (as with any other asset) can also be apportioned to the most appropriate commander as the JTFC see fit (normally on the advice of the Air Specialist - the JFACC (that need not necessarily be RAF)). Could be under the JFACC but apportioned to the JFLCC or JFAmphibCC for CAS.
As for JHC, the same really. AH are normally under the JFLCC whereas (I understand) SH (like other assets such as JNBC Regt) are now coordinated directly from JFHQ (with embedded SHF HQ elements). Could be apportioned to (for instance) JFLCC or JFLogCC as the need requires.