Whilst there are a number of us who frequently find boringguy's posts abrasive-I have to say I agree with 100% regarding this post.
With the info you have given-I would say that your marriage isn't in a place to manage itself much less poly.
lies of omission are lies and lying does not breed the trust required to make poly function.
It seems people (me included) seem to find it hard to learn that lesson without trying it themselves.
But-the bottom line is that both you and he need to get brutally honest with yourself, each other and the rest of your world if you are going to get to the poitn where you can learn what it takes to manage such emotions as jealousy, envy, etc.
"Love As Thou Wilt"