Which really is not a huge issue .. since you have to clear US Immigration/Customs in MIA .. you will be getting off the plane and then thru formalities .. recheck your luggage.. reclear security and go to the new gate.
Where CHG becomes a pain is someplace domestically where you think you are on AA12345 from A to C with a stop in B.. only to find out you are on one plane from A to B and then another from B to C.
In your case .. it really means minimal as you have to get off the plane anyhow.