What can I use to prove residency?

[AlinaH 38]

I'm in the process of removing conditions on my greencard. If all goes as planned, I should have my 10-year by the end of January, I'm figuring.

My husband (USC) and I may have the opportunity to do a volunteer project through our church. Basically, we'd be living in Amman, Jordan and teaching school for a little less than 1 year - approximately 10 months. We would leave in August 2014, come back for about two weeks in October, and then leave again and not return until sometime in June 2015.

I know that being gone over 6 months and close to a year, it is likely that I should apply for a re-entry permit, correct? Does it make any difference that I would be coming back in October for two weeks (making the second leg of the trip about 8 months)?

My main question is, what can I use here to prove residency? We have every intention of residing in the United States, apart from those 10 months. We currently rent an apartment but will be letting that lease go if we get accepted to the project. We own a car together - would it help to keep it registered and insured during that time? What if we had a storage unit? Can our joint bank account be used to establish residency, even if it doesn't have much use during the time we're gone? What else can I use that I haven't thought of?

Thanks in advance!