this wouldn't be double jeopardy. It would be a second instance of him refusing to turn over the passwords. Just as you can be tried twice for murder twice if there are two separate murders, you could be tried twice in this situation.
This was (?) the way the USSR used to handle conscientious objectors:
They would send you a letter to go serve in the military,
You would go to where you where assigned,
You objected because of your conscience,
They would then send you to a force labor camp or mental institution for a few years,
The hard work, unhealthy food and living conditions,
lacking health care, medical experiments, and violence among convicts
would often destroy your physical and mental health,
Then when you where released,
They would send you a letter to serve in the military.
Unless, naturally, your conscience would no longer object to serving in the military…
Disclaimer: IANAL. Disclaimer: IANAA (I Am Not An American)
Assaulting the same person twice would still be two different assaults. Stealing a truck, getting caught and punished, and stealing the same truck again would, to my understanding, not be risk-free, legally speaking. I suspect the same would probably apply here, though given how unintuitive the law is, especially in this area, I may well be dead wrong.
Edit: To clarify, my point is that if the law amounts to "Refusal to turn over requested passwords => jail time", this would seemingly constitute a second refusal, even if the requested password was the same.
By the same logic, if the authorities had asked him one hundred times in the first interview for his password, and he'd refused one hundred times, then he could be charged with one hundred counts of the offence and put away for 30 years.
The courts aren't run by robots. If it's substantially the same instance of the offence, he couldn't be tried again.
What rationale do they have against double jeopardy? Without it you can make any jail sentence be until someone's death. You can be given a speeding ticket for the same offense until you have no money left.
You can certainly be tried for the same crime twice. You can't be tried twice for the same criminal act. Arguably, if they ask him again after doing his 16 weeks, it's a new action if he refuses to comply.
It's not a trial. It's refusal or follow a court issued order, the punishment is contempt of court. They don't need a trial in that case... the judge that issues the order can simply judge whether or not you're complying with it.
In all these scenarios, you're screwed the moment you find yourself in court (actually probably long before then when you convince some law enforcer that you're doing something wrong) Judges and lawyers aren't going to be hip to this hypothetical plausible deniability game.
A drive isn't an extension of your brain or your relationship with your wife. It's physical evidence. The only thing that makes it different than say a really big lock on the door of your house or a safe is the effort it takes to circumvent when a court agrees to admit the evidence. Almost never is that evidence used alone.
There are subtle issues to the meaning of the evidence provided, like you might not need to give up the password and thus decrypt everything else encrypted with it, you might just need to decrypt the data in question in a convincing manner to the court. Being able to decrypt the drive doesn't have to prove that you are responsible for the contents.
He's not being tried for refusing to hand over the password - he's being held for contempt of court or similar, which can (and does) go on indefinitely. He's free to leave any time as soon as he hands over his password.