Rem started doing the same thing - I've taught him "off." It's very simple, say "off" firmly, treat and praise when he obeys. But here's the trick - I also taught him "up." Maybe it'll come in handy one day, but really I just wanted to drive the "off" concept home - if he knows what up is, he knows even more what off means. And it enables me to practice by telling him up and then off. He's mastered it. He'll still attempt to jump up, but a quick "off" and he's right back on the floor. He's only 4 months old, so I expect with more training, he'll stop it completely soon.
Combined with leave it, it's highly effective. So even if he does jump up, "leave it" and then "off" will ensure he not only gets down, but doesn't touch anything. Rem knows leave it well, so he has never eaten or grabbed anything off of a high surface. He just investigates, xD.
I would know if it happened if I were in another room because I'd hear it - he's a big, oaf of a puppy and he makes a lot of noise just doing anything. I have never heard him do it when I wasn't around. But I also make sure I do not leave food of any kind on my counters. But I have so many other pets that such a thing would be foolish of me, anyway. I have left chews and stuff on them - and off must work, because he knows they're there, and leaves them alone. If the command was a failure, I'd keep finding him with the bones, but so far, I haven't.
My late Great Dane, Scout, who I lost in August, truly couldn't help it - his head naturally stood taller than the countertops! He didn't even have to jump up! Always had things disappearing when he was around!