"... on our monthly statements it’s only in his name ..." -- means the mortgage loan was taken out only in his name. Hence he is the only one that is obligated to make the mortgage payments and thus the only one that can claim the mortgage interest as a deduction.
"... we are both on the deed ..." -- means that the title on the deed is in both names as owners. If/when you sell the house you can split the proceeds any way the two of you desire.
