Yes, you can share lists so that any tasks put therein are effectively both of yours.

You can also share individual tasks, but I'd think lists would be more effective for you. At least, they are for my wife and me. :)

Thanks; that's helpful but all of our tasks are in the inbox and it appears that you can't share the inbox. Is this correct? Any easy workarounds?

Correct; the Inbox is more or less a special folder (for receiving sent/emailed tasks) and cannot be shared. You can move all tasks to a folder—e.g. "Shared", "You & Me", etc.—and share that list.

I have actually only created two lists—"Mine" and "Shared"—and the only difference is that Shared is the one where I put tasks for both my wife and me.

Hope this helps!