Joseph: I’m curious, are there trust issues in your relationship? If there are, get help now! I would never think to ask such a question.
As for me, my computer is open day and night, except Shabbos, as is my e-mail. My wife could look at it if she wanted without my knowledge, but she doesn’t and I don’t look at hers either. We have no such need, especially when you know there is nothing to hide.