I recently spent some time experimenting with different ways to program partially-hidden navigation tabs in Storyline. There are a couple of ways to do create tabs like that and they all have different end results. Here are two examples:
The tabs in the second .gif have the best-looking results (in my opinion) and they're a bit tricky to program.
Check out my blog post for a discussion of different methods and a .story file for a demo with the tabs with a smooth hover movement.