punctuation - Comma placement in a "parenthetical expression preceded by a conjunction"

I was reading Strunk and White's Elements of Style, and I disagree with the comma placement in the following example:

If a parenthetic expression is preceded by a conjunction, place the first comma

before the conjunction, not after:

He saw us coming, and unaware that we had learned of his
treachery, greeted us with a smile.

To me, it makes more sense to place the comma after "and", not before it. That is, to write:

He saw us coming and, unaware that we had learned of his

treachery, greeted us with a smile.

In the above modification, the main sentence is "He saw us coming and greeted us with a smile", which is perfectly valid in structure; the parenthetical is "unaware that we had learned of his treachery".

I know that a lot of people have disagreed with Strunk & White's writing and claim that it's overrated (and frankly, I sort of agree with those people), so I'd like to know whether this example would also fall into the category of "things Strunk and White got wrong".

Is placing a comma after a conjunction in a parenthetical expression, such as in the example above, grammatically correct?