How to deal with separation anxiety?

My daughter has been at a stage of separation anxiety ever since she turned eighteen months.  She is now thirty-two months old and it has only become worse.  I used to be a full time employee and my husband went to work part time and he was in school full time.  We would juggle our schedule so our daughter didn’t have to be put in day care.   She would cry when I went to work but not when her dad would leave.  Currently, my husband is still in school but works full time and I’m a stay at home mom.  Any time she notices my husband leaving without her she cries and throws a fit.  He is resorted to sneaking out as quietly as possible.  Even when it is his day off and he has spent all day with her if he tried to go outside without our daughter the crying starts.   She doesn’t like me to go anywhere without her as well most of the time.  She is very independent and plays alone periodically during the day without needing mommy to entertain her.  She just gets very upset if she thinks one of us is leaving without her.  I have patiently explained to her daddy has to work.  We have tried having him tell her goodbye, we have shown her where he goes but nothing works so we just have resorted to the sneak method.  Her fits don’t last long as I have become good at distracting her but the guilt my poor husband feels by leaving her is weighing on him.  I’ve been told she will grow out of this but when is the question.  Does anyone have any suggestions on how to make this anxiety go away?