Everytime I create an object in Inventor, it turns sideways when I export it to Revit. I am using Autodesk Inventor Professional 2013 and Revit Architecture 2013.
I'm not a Revit user, but Showcase does the same sometimes. In Showcase there is option to select the Original Up Axis of either +Y or +Z or Auto-detect.
What is your workflow to export from Inventor?
Check this link you might find your answer. There is a small tutorial with attached a template file to try it... Although a comment in the end of the tutorial will give an alternative solution...