It is hard to open up to parents. Believe me I'm going through that right now. You just gotta let them know that they can tell you anything. Though you may get upset..don't throw them to the dogs for opening up to you.
They need to know that you will always be there for them though good or bad. And if you get upset let them know its cause you love them and just be honest with them. The honesty and communication will make its course to you gradually until it becomes a second nature to them.