The GI benefits are income, but you may qualify for a chapter 7 even with that income. The creditors cannot make you cash out the benefits so they will likely be unaffected, but you need to talk to a bankruptcy attorney in New Jersey.
Chapter 7 permits the debtor to get rid of all of their unsecured debt without having to make payments to that debt. It is not a good choice for people who are behind on their mortgage and want to save their house from foreclosure. It is an excellent choice if you want speed and simplicity.
You must qualify for a 7. The tests are income versus ALLOWABLE expenses (term of art...need a lawyer) "liquidation" (do you have equity in property that is not protected by an exemption (law stuff again) and the "means test"...one of the stupidest things Congress has ever thought up (and I am a conservative Republican) which asks are you an above or below median (half above/half below) income household.
Chapter 13 is a bankruptcy where you are required to make a monthly payment for 36 or up to 60 months. The basis of the payment is never unsecured debt. It is affected by the tests outlined above. Filing this bankruptcy will stop a foreclosure and allow you to repay the mortgage arrears at zero percent interest.
Disclaimer: This answer does not constitute legal advice. I am admitted in the States of New York, New Jersey and Massachusetts only and make no attempt to opine on matters of law that are not relevant to those three States. This advice is based on general principles of law that may or may not relate to your specific situation. Facts and laws change and these possible changes will affect the advice provided here. Consult an attorney in your locale before you act on any of this advice. You should not rely on this advice alone and nothing in these communications creates an attorney client relationship. The opinions expressed herein are those of the author only and the fact that he has worked as an Assistant District Attorney; State Supreme Court Clerk; Special Assistant United States Attorney (Hawaii); Assistant Cornell University Counsel or Judge Advocate, United States Marine Corps should not be relied upon to assume that these statements reflect the policy of these organizations.