Me and my husband share everything and keep no secrets. But if it was someone else's secret, then that is different. That is someone else's, not mine. So no, I would not tell him.
A pal of mine confessed in floods of tears that she had had an abortion at 16 weeks, and told everyone it was a miscarriage, and I am the only person who she told. Her husband doesn't know, her mother, her 2 sisters, her other 2 (teenage) children; no-one.
I never told anyone, not even my husband. As I said, it was not my secret; it was hers.
What's more, my husband knows her, and her husband, not really well, but he knows them, and he sees her brother at the pub some weeks. So I wouldn't want the risk of him dropping it out to them.
I love him but he has a big gob sometimes. I peeped into our daughter's facebook once, as she was having issues with a girl at school, and I said 'you cannot tell her!' (She kept herself logged in, so I was able to have a peep to see what was going on.)
And what does he go and do? He mentions I looked in her facebook. She went absolutely ballistic (understandably...) and changed the password, and never kept herself logged in again. When I said 'what the fuck did you tell her for? I told you not to!' He said 'I forgot you told me to say nothing didn't I?!'
Forgot my fucking arse!
He has done similar things on 3 or 4 occasions too, blabbed when I told him not to. One time several years ago, I got so drunk I was sick (not proud of that, but I only had 4 glasses of wine.) And I said 'don't you DARE tell anyone, particularity the kids!'
You can probably guess what happened!
'Your mum is a right old lush! You shoulda seen her sprawled out over the pub table, and then vomiting all over the bathroom!' he said whilst laughing his head off.
Sometimes I think about doing something similar to him, but I'm not a cunt. 
Well he ain't a cunt really, he just behaves like one now and again!!!