Two heads are better than one
I think you should have your own project and action lists but some projects are bound to be shared.
The Weekly Review (as ever) is critical. You should do your own Weekly Review and then do a joint Weekly Review to cover the shared projects to decide who's got the Next Action.
I don't speak from personal experience as I haven't yet persuaded my wife to take on GTD but I do get her involved in a joint Weekly Review after I've done mine.
David Allen may have some advice as he and his wife obviously both use the system.