It will be a joint command, officers will get a participation medal, a legion of merit, and credit for serving in a joint unit.
Their prime directive will be that no soldier ever come into contact with an illegal. Weapons and ammunition will be highly restricted.
The official ROE will be vaguely-worded with conventional diplomatic niceties.
The interpretation on the ground?
All armed persons not belonging to US forces will be assumed hostile - and will be fired upon if they threaten US forces. That will include Mexican police and army...
Cross-border attacks from the Mexican side will get lethal responses and the border might get a little fuzzy in such cases.
Representatives from the media will be excluded from active areas "for their own safety".