I hesitate to comment because I suspect it will just lead to trouble. But ausielass and rhogg have broken the soil up a bit, so let me speed the plow along.
Posts like the OP here are just a sad puzzlement to me. The idea of man hiding something like this from his wife, of her "finding him out," like a naughty schoolboy who has missed curfew, it just makes me shake my head.
It's one of my foundational principles that "no one understands anyone else's marriage," so if this kind of arrangement suits you, well enjoy, I suppose. Worse than being the husband in such a marriage must be to be the wife.
My view -- and, frankly, my experience of most men and women, across religions and cultures -- is that marriage works when there is sacrificial leadership and real trust, love and a responsibility. Too many men are afraid to be the servant leaders of their homes. Too many women are afraid to say they want -- what they long for -- in their heart of hearts, for their husbands to be the servant leaders they were meant to be. To be MEN. I can tell you the peace, fun, security, power, fulfillment and pure joy of a marriage founded on those ideas is not to be compared to the struggle and angst of a union that ignores them.
This isn't as simple or base as "he's the boss," even though those who oppose these ideas it often create that straw man to knock down. (I don't doubt someone here may try the same approach.) But it does embody roles that are different, one from the other.
Real women want to be married to real men; always have, always will. Simple as that. But after 40 years of brainwashing in western developed society, stating these simple truths is dangerous stuff.
(That's the secular side. I come at this also -- and more fundamentally -- from a Biblical perspective, but I'll forebear a discussion of Ephesians unless someone says they're interested.)