The company my husband works at gives you 1 week vacation time after a year. It says in his company policies that if they want to take vacation they have to get a form and fill it out then have there supervisor approve it. My husband filled his form out and had it signed but when it was sent to the office the office denined it. They have 2 shutdowns a year. 1 at Christmas and 1 over the 4th of July. They are telling him that he has to save the vacation time he has occurred for the week they will be shutdown over the 4th of July, that way they don't have to pay out unemployment. Is this leagal to tell him when he can take it.

Yes, it is. They have no legal obligation to provide vacation, paid or unpaid, at all; they get to make the rules about how and when it is used.