Thanks for your explain! Now I've got it! ... Thanks again"I don't believe it" expresses no doubt. The speaker simply doesn't believe it.
"I can't believe it" leaves a little room for doubt. The speaker may have a little doubt. This is also used to express astonishment. For example, "I can't believe she died!" doesn't mean that the speaker doesn't believe it. The speaker knows it's true, but is astonished or shocked.