I am not a tax attorney, and I have found few people that can accurately deal with your situation. I am a sole proprietor (independent contractor) and I have had foreign contracts where I was physically not present in the USA for years at a time. The companies paid my USA company (my business bank account in the usa), so I have records of income.

Are there any US deductions taken out of your check? If not, then you may be considered an independent contractor. If this is the case, then you should file your old tax returns, with schedule C 'profit or loss from business', and also claim form 2555 'foreign earned income'. This will give the loan people the proof of income, but it will also bring you a bit of tax problem... as an independent contractor (or business owner), you are liable for self employment taxes on the full amount, regardless that it is foreign earned. This means you may owe penalty and back taxes for the last 5 years if you file as such.