What structures in cells contain DNA and proteins?

The structure in cells that contains DNA and protein is the nucleosome, found in the nucleus. In the nucleus of the cell, DNA is exists in the form of a long helical thread. It order to fit inside the nucleus, the DNA thread must be compressed enough to do so.

The cell accomplishes this by wrapping the DNA thread around a protein called histone. A single unit of DNA and histone octamer (called octamer because it consists of 8 proteins) is called a nucleosome.

The entire stretch of DNA in an average human cell is about 2 meters in length and would never fit inside a cell if not for histone proteins.