No, and I don't recommend it. When two people are responsible for something, nobody is. Everyone should have their own separate system.
You will likely have shared projects; in those cases it might be on your Projects list and your spouse's Projects list. Or it might be on just one of your lists if one of you takes primary ownership.
I think there was a similar thread on this topic in the past. Try searching the forum to see what others had to say.
- Luke