The phrase "midnight sky" refers to the dark sky that you see during the middle of the night. It's the time when the sky is usually black and filled with stars. Full definition
The search for neutron stars has intensified because of a relatively small area, low in the northern midnight sky, from which the strangest radio signals yet received on Earth are being detected. (sciencenews.org)
The profusion of newcomers — including even ninth - magnitude stars — is especially dramatic when sweeping binoculars along the eastern or southeastern midnight sky this month, as the Milky Way is rising. (discovermagazine.com)