Quoting MysticWitchKat:" This relationship is sooooo unhealthy."
Honestly checking someones phone and whatnot is not healthy. You don't trust him and it doesn't really seem like either of you are working towards trusting each other.
Go to counselling, sit down and talk it all out. It's not a healthy relatinoship and it's not a healthy environment for the children to be in. Not saying you are bad parents, but they take relationship cues from their parents, and do you want your kids to think that that relationship is the best relationship to be in?