The meeting dragged on into the night.
彼は夜中働いている。
He works at night.
He often works during the night.
深夜 specifically points to the late-night hours (after midnight), whereas 夜中 (やちゅう) refers to the nighttime period more broadly.
日中 means 'during the daytime', the direct opposite of 夜中 (やちゅう) 'during the night'.
Written identically, 夜中 read やちゅう means the general nighttime period, while 夜中 read よなか means the specific 'middle of the night'.
Compound of 夜 (ya, 'night') and 中 (chū, 'during'). The reading やちゅう is the on'yomi combination.