Newb Illustrator fill question

I traced a coffee mug with the pen tool. Then I traced the inside of the mug handle, creating two paths. I want to fill the mug but not the inside of the handle. No matter what I do - arrange the handle path forward - non zero - compound path - all the suggestions on the internet - filling the mug, fills the handle path. How do I make the inside of the mug handle no-fill?

Nancy L. Smith
President
Sutton Bay Media Company