Another way of saying that is
while the tune is in Edorian (3rd and 7th flatted)
the 1st measure (ascending) of the B part
is in Emaj and
the 2nd measure (descending)
is in Edorian
I think that's the way
it's usually written in the books

In Edorian only the 3rd and 7th notes are flatted.

It's technically not quite a "melodic minor"
(same as a "harmonic minor")
In a melodic (harmonic) minor
the 7th note is not flatted
but the 6th is flatted since it is a minor key.
But this is not Emin but rather Edorian (6th is not flatted).

Got that? Some arcane music theory! Sorry

Cheers, S. in Seattle