Can "Your Majesty" and "His Majesty" be interchangeable?

Question

From the TV Show Cursed, Merlin is talking to King Uther.

Merlin: ...Father Carden and his paladins are dull vessels for these old hatreds, and nothing more. However, if His Majesty would allow it, the Shadow Lords may be able to offer some service here.

King Uther: Shadow Lords? It's a bit late for your enchanters to help us now.

Merlin: Not necessarily. They can pull certain strings to slow Carden's march. There are Shadow Lords at every level of socie--

King Uther: [yells] We want rain, Merlin! To hell with your Shadow Lords.

Merlin: I will redouble my efforts, Your Majesty.

King Uther: Yes, do.

Answer 1

Your Majesty is used when addressing the King directly. So in this sentence:

I will redouble my efforts, Your Majesty.

"Your Majesty" is correct. ("Your Grace" or "Sire" might work, depending on the exact protocol or etiquette observed in the particular era and in the particular realm.) It couldn't be "His Majesty".

His Majesty is a way of talking about the King in the third person. For example:

His Majesty has ordered that no one is to leave the Kingdom until the perpetrator is found.

You couldn't have "Your Majesty" here - or rather, if you did, it would change the meaning from "The King has ordered ..." (addressing a third party and informing them about the King's decision) to "You have ordered ..." (reminding the King of his own order).

However, to some extent, yes, Your Majesty and His Majesty are interchangeable. The reason is that in very formal usage you can effectively address someone in the third person, as in "Would Sir like to see the wine list?". So I can see that "If His Majesty would allow it" could be (in context) effectively synonymous with "If Your Majesty would allow it".