Middle Of The Night
Late At Night
The deep night is the middle of the night. It doesn't get any deeper than that before you start coming out of the night to start the next day.
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well.
What's up this late at night?
I got a bit hungry in the middle of the night.
The environmental refugee bears crossed the border late in the night to find something to eat in a new country.