Thanks GiveLove!
I cannot live with someone who is deceptive either. In my view, the omissions I've been having to deal with are remnants of his past habits. My hope is that he will learn that there is no reason to not tell the absolute truth, or to fear what I might say about it. So I'm giving him some time to do that.
As for the not taking it personal part, what I meant was that I need to remind myself that he doesn't lie to me because of me or something that I do/did. He lies because it's a habit, he lies out of fear or denial. So I shouldn't take it as something that is directed solely at me. It's just the way addicts are, and something they need to unlearn in recovery.
So far, he hasn't lied to me about anything... Just omissions, and they haven't been important ones. We'll see how it goes, but I have a very clear boundary on that and I'm not willing to compromise on it.
What I need to do is think of a deadline or milestones to measure progress, but I don't know what's realistic.