Double Tab Navigation – What do you think of this experience?

The double tab is a strong system. It uses very little vertical space and communicates very effectively the idea of ​​a hierarchy. Nested tabs are a big drawback, though. Your design is pretty good, but it's still a bit busy.

My favorite solution is to use a small triangle cutout for one of the levels. For example:

model

download bmml source – Wireframes created with Balsamiq Mockups

This has the same advantages as the tabulation model, but has a different look and is a bit more subtle, which suits the second level of the hierarchy.

Finally, I can not say if this applies to your interface, but just in case: do not use hover to expose the sub menu of the tab. The layout of the tabs is excellent, as long as you stick to the metaphor. If a tab is active, everything on the metaphorical paper map must belong to this tab. If, at any time, you display the A tab above the other tabs, with the contents of the B tab still present, you are breaking the rules of your own interface metaphor and your interface suffers. You can use a drop-down menu on the tabs (what you seem to have), but only change the active tab as it actually changes (content and all).