Schilthorn and Jungfraujoch in ONE day?

In theory, you could, if the weather cooperates. But I wouldn't advise it. It's just too much. Pick one or the other and spend the rest of the day hiking/walking and enjoying the beauty all around you.

I agree 100% with Carroll. This is possible, but not desirable, and before going up either one, make sure the weather is good enough to justify the cost.

As for how long each one takes, that depends on you. There's the trip time itself, plus the time you spend on the various attractions at the top, as well as admiring the views. Given the cost, you won't want to rush your time at these places.

Schilthorn has an exhibit on the filming of On Her Majesty's Secret Service that I found interesting, but others may not. Then you stop off in Birg on the way down; on the day I went, my view from the Schilthorn itself was cloudy, but from Birg it was crystal clear, so I spent some time there before descending.

Jungfraujoch has various sections; again, one viewing area was all clouded over, but when I went out on the glacier the views had cleared, so I spent some time there. I went faster through some other sections that others may have enjoyed (there's several with various photo ops that some would find hard to resist; I wasn't as interested in these). I also found that the altitude of the Jungfraujoch made me feel a bit sluggish; I was moving a bit more slowly than normal for much of my time there. And afterward, I was quite tired for much of the day.

If you do hit marginal weather or don't want to spend to much money, consider the Allmendhubel. It's MUCH cheaper than the Schilthorn but you get to see the three peaks (peaks themselves are not visible from Mürren). There's some nice walks at the top, so you can spend some time up there, but.since it's not expensive, you won't feel obligated to "get your money's worth" by spending lots of time, if you're in a hurry.

You don't need to do both. The Jungfrau is rather like a "resort" because there are just so many restaurants, shops, observation decks, outside activities like sledding and ziplining and snowboarding.

The Schilthorn is MUCH less and, in my opinion, probably a better use of your time. It's also fraction of the cost of the Jungfrau.

It takes an hour to an hour and a half (depending on where you start) just for the train ride in the tunnel up to Jungfraujoch. Then the same for the trip down. That would eat up a lot of your day.

Thank you all for your input. It is my wife and I's 33rd wedding anniversary trip so I want it to be perfect!
THANK YOU

As per the other comments, definitely too much for one day... On the day we went up to the Schilthorn we spent over five hours up there. It was a gorgeous sunny day and just couldn't pull our selves off the mountain... That was back in 2013, and now they even have more things to do and see up there...
Unfortunately the following day when we went up to Jungfraujoch by the time we got up to the top it was a blizzard and a white out so we couldn't see the glacier. We had no view at all for that matter... But it was still a great experience... And we still spent hours up there and the round trip took us about five and a half to six hours.

It is my wife and I's...

Must....let..it go....