My husband does not share his email password with me. Once he needed something urgently from his email while he was out. But he would not give me his password. He said there is some confidential work information that he cannot disclose to any one. If I am standing next to him, he will close his email. It makes me feel anxious if he is hiding something from me. Is that normal or I am overreacting?

For me it would worry me to. Maybe he is hidding something. Personally i share everything with my husband but he hids things from me to so either its a guy thing or maybe there is more to it.

Short Answer is Yes. Speaking as a Husband. It shouldn't be that big of a deal to have separate passwords. BUT. If there are other things that are going on that make you uncomfortable or make you distrust someone, you have a right to question it. If your spouse loves and respects you, they will want to help alleviate your fears. Showing you their emails or passwords should not be that big of a deal. If your husband didn't want you to look at his "confidential work" he should still be able to trust you enough to know that you would not look at it. Does he trust you enough? If he does, then all his excuses don't add up.
If my wife wanted to see my password or email accounts I would let her. There might be a few embarrassing things she would see but nothing that I am ashamed of. As of now she doesn't know that I come on these message boards. I will eventually tell her. It is a part of my healing process. It allows me to express my feelings unencumbered. When I am more comfortable with it I will show it to her.
Hope that helps a little. Just trying to give a little insight into how some of us men think.

share everything. the only instance where secrecy is acceptable is if one of you works with top secret government information. seriously.

think about it. what is the other person trying to hide?

take it from someone who has cheated and is currently being cheated on. adultery can only happen in the dark. secrets are the thing that can kill a marriage.