Forget about 'unbelief'. It is only used in some specific religious contexts. As a word, it doesn't really exist in everyday English. Nobody ever uses it.

Disbelief is the state of not believing, or refusal to believe. While unbelievable is when we think something is so hard to be believed. For example, a) His disbelief in that matter would ruin him eventually. b) Your words are unbelievable, This hurtful truth is very unbelievable. I hope this help, alex.

Unbelief- is the lack of belief or refusing to believe. For an example, The dog was in disbelief when there was no more food. Disbelief- feeling of something that is not real or cannot exist... For an example. Atheists believe that God does not exist...They believe it is impossible for spiritual beam to exist and turn water into wine.. According, to them humans came from Apes and the universe.