I think it is your business to know. As a married couple, I think both parties should be transparent with their financial dealings/credit/bills etc.
I've read too many stories of one spouse using a secret card to hide their *extra-curricular* activities and the other getting burned emotionally and/or financially.
What is the purpose of getting one of these if you have enough credit on other cards? It doesn't make sense nor does, in my opinion, it bode well.
If there was a way to find out what he is purchasing with it, I would do that. If not, I would straight out ask him.
So, my advice is to stop obsessing but get to the bottom of it.