As far as I know, the US is the only country that requires it's' citizens to pay income tax even when they live and/or work in another country. So do check with the IRS directly - it's just a phone call and it is what it is.
Ilhamo is correct that you may well qualify for a credit if you stay on top of your paperwork and fall under the income limit - check the IRS website and browse ex-pat forums.
Also, bear in mind that immigration laws may change at the drop of a hat - both for your husband and for you, they might enact a change a month before you leave, so be prepared and have a plan B, just in case.
I'm mentioning this not to scare you but to counsel you to be 100% aware of what is going on with immigration in both Germany and the US at all times regardless of where you live, the law is the law.
Ignorance is not bliss when it comes to immigration - in any country.
In my opinion, the smart thing to do would be for your husband to get his citizenship before he leaves the country - dual citizenship is the best route if you still have some connection to Germany and know you will be going back from time to time.
If he goes back to Germany for an extended period - not sure what the critical time frame is at present for a green card holder, either 90 days or 180 days is the limit, he will be forced to start the entire immigration process once again - his alien card will become invalid. (You can get an extension, but only if you get it approved by immigration before you leave, illness of a close relative is a qualifying reason for instance).
Doesn't matter if you worked in the states for twenty years and paid taxes - you lose your permanent residency and you have to have a sponsor who makes X amt of money, etc. and start the immigration process all over. Not sure about the student and specialty work visas, but they seem to be even more restricted.
The German consulate in your state may be able to help you with a number of your questions and your Visa requirements. Call them for an appointment or e-mail them with your questions.
They will usually also be aware of what laws are about to change and their impact on your stay, work permit if any, etc.
At any rate, this is a fabulous opportunity I'd certainly take advantage of. You will be glad you did, Germany is in the heart of Europe - you can go to Paris for the weekend any time you like:) and most everyone there seems to speak English.
You'll have family at your disposal to help out and make sure that all of you have a great stay and hopefully lots of travel and great educational experiences.
Language - study-up and make sure your kids are as prepared as possible for a smooth transition, they'll pick up the rest quickly enough. I grew up in Germany but my son knew almost no German at all at 15. (Long story) When I went back to Germany for several years, it took him only three months to become fluent since he was fully immersed and both my Mom and I refused to speak English with him for the most part - he hated us for a month:) but then one day it was like someone flipped a switch, he spoke fluently.
Writing took longer, German is not an easy written language.
Think about what you would most like to see and do while in Europe/Germany, then find a way to make it happen:). We all have different expectations and enjoy doing different things as individuals and as a family - living abroad with familial support is a gift, make the most of it.
Giving your children an opportunity to get to know their grandparents on the other side of the pond is a wonderful thing, a privilege not everyone can afford.
... and yes the health insurance is a huge bonus, so you might consider "playing medical tourist" while you are there, making your trip that much more profitable to you. I do that even when I'm just there for a long visit.
It sounds like you are already doing your due diligence, the rest is cake:) - so, GUTE REISE und VIEL SPASS.