DNA contain negative charge because the presence of phosphate group. Generally, hydrogen is not shown in DNA structure. 

DNA

There are 3 hydrogens in phosphoric acid, each of them leaves as:

1 H joins with 3' -OH of previous nucleotide to form $\ce{H2O}$ during DNA replication.   
1 OH joins with H of next nucleotide to form $\ce{H2O}$ during DNA replication.   
1 H is released as $\ce{H+}$ (remember it was phosphoric acid), hence giving rise to the acidic character of DNA (remember it is deoxyriboNucleic acid).