I have found that there are many projects that my partner and I may share, but there are very few Next Actions within those projects that we both need to be responsible for. ("Need" is very different from "could be.")
We recently moved into a new house, and with that came all sorts of projects. For "shared" projects, I made one master list, divided in three parts: tasks for me, tasks for him, and tasks for either of us. I gave him his list (he doesn't GTD) and went ahead tackling mine. We split the "either of us" tasks between us after discussing them.
I would not suggest that you share processing inboxes, weekly reviews, etc. You are two independent people and you each may prefer your organizational system with particular nuances. A weekly check-in on truly joint projects is all that's necessary.
David Allen mentions that if he's working and his wife has a non-critical request, she drops it in his inbox and leaves him undisturbed. I love this. You should each have an inbox that the other trusts is processed regularly.
A big part of living with someone is deciding what's really important and what's not. It wasn't worth an afternoon of debating where each of our eight dry-erase boards would go on the office wall, when he could take responsibility for that project and I could spend that time arranging the racks in the storage room. In theory, "Arrange Storage Room" is a joint project, but it made more sense to divide and conquer.