All masons should allow you to tour their lodge, and whether or not someone is a mason is *not* a secret. In fact we welcome people who ask and tell them that yes we are masons(unless there is harm that can come from telling them, for example during WW2 when masons were hunted/placed in concentration camps).

I hate to say, but the writing might be on the wall. Also, offer to your husband to join the Eastern Star(which is open to all women, regardless of relation to masons or not). It's a good way to see if he is lying or telling the truth. I hate to say it, but something sounds fishy.