"under the moonlight" is correct and usable in written English. You can use it to describe a scene or setting in which the moon is visible, or when something special or magical is happening. For example: "The couple shared a romantic kiss under the moonlight."
"Under the moonlight or generic fluorescent light, people's expressions glow and they look more beautiful".
Under the moonlight, they drove down mazy roads cut through the fields.
He enjoys long walks on the beach and dancing under the moonlight.
This is the music they grew up with, music that was played under the moonlight.
The snow falling on Newburgh's Washington Square glows under the moonlight.
Foam from the lapping waves glows the same incandescent white under the moonlight.
Skylights in the bedroom mean you can sleep under the moonlight.
At last, they are alone together on a beach, in swimsuits under the moonlight.
Then the fireflies would emerge, thousands and thousands of them, and under the moonlight they would all flash in unison.
When Ms. Larusdottir did, you were reminded that the song is in fact about giddy, secret love under the moonlight.
"We look forward to revealing the Alta Moda Summer Night's Dream in our fairy garden under the moonlight," read handwritten invitations that were delivered to clients' rooms.
Ludwig does not simply clarify my doubts with English writing, it enlightens my writing with new possibilities
Simone Ivan Conte
Software Engineer at Adobe, UK