Hi Julia. I didn't realize that you'd already told him that you knew he was involved and moving in with OW. So, scratch what I said. It's when the other person is a secret that the lying gets to be a real problem on top of the integrity problem.
He lies by omission. He says he's going on vacation, but, he leaves out a lot of information like that he's taking OW with him etc. He asks you for something like the car without telling you he wants to sell it and so on.
If you feel you're communication is truthful and only inadequate. Say so. Tell him that he needs to behave like an adult and start talking to you about the house etc.
In light of your latest, I'd say you are definitely in the sweet spot of what you can be doing and I wish you all the best.
