They don’t work together, and after trying the new interface, I found that I couldn’t regain my multiple inboxes. So I googled on Google to find a way to fix Google’s new mail interface and found that Google couldn’t tell me but someone else could: Thank you lifehacker commenters. If you’re using google labs multiple inboxes and find it missing because of the new tabbed design, do this: Make your inbox view “default” and then uncheck everything but the primary tab. Multiple inboxes will be back just the way you had it previously.
It’s a shame. I actually like aspects of the new interface. If they’d let me define the tabs myself, preferably with the freedom that multiple inboxes gives me, I’d use it in a heartbeat. But you can’t even rename them? Sure, I can change the filters, to a small extent, but why should I have to remember that I repurposed “forum” into, say “business email”? Why aren’t they letting us decide what to call them?