My son recently confided in me about some of his behaviors.
Fortunately I"ve never been put into that position. From the time the boys were young most 'big' talks were done by both of us, either together or separately. I don't think I could ever promise to keep something big like drugs or other illegal activity a secret from their dad. Now if it was something 'male related' I could understand. For example once older ds thought he detected a lump in his testicle and called dh about it; dh, of course, told him to get it checked out. Older ds did tell me about it later after it all came back fine but didn't want to worry me at the time. There was also a question/issue he talked to dh about a couple years ago that at the time he asked dh not to tell me about but again it was kind of a male health thing. Had I had daugthers and one of them had come to me with questions or concerns about their period or something but didn't want me to tell dh out of embarassment I would likely have respected that unless it turned out to be a major health issue.
I think when you're married it's a bad precedent to set to keep things from your spouse.
I like those "we are a unit" words.
I handle it exactly the way you do.
My dd's are 27 & 30, and they do occasionally remind me
my kids know that not only do I tell DH everything, but the deli guy at stop and shop too.
I don't think my kids have ever said "Don't tell Dad."
When my dd#1 was about 4 years old I discovered little finger prints in the stick of butter on the kitchen counter.