Just to give everyone an idea about costs:
Surgeon: $10,000 (includes consultations, models, x-rays, and surgeon)
For insurance to cover a procedure, medical necessity must first be established. The surgeon takes measurements, pictures, x-rays and models of your teeth and submits a letter to your insurance company stating that this is not being done for cosmetic reasons, rather that the condition is abnormal enough that orthodontics alone cannot fix the bite and/or that you have other underlying conditions that are made worse by the poorly positioned jaws.
I had the benefit of submitting a letter from my ENT stating that my sleep apnea would improve with correct positioning of the jaws.
Some insurance companies will deny you outright because they do not cover jaw surgery (cost savings). Other insurance companies will have a review board, where your case goes before a group of medical specialists on behalf of the insurance company and they either accept or deny you on a case-by-case basis. Other insurance companies just require certain proof (the x-rays, measurements, photos and models) and automatically approve you.
You do have the option to file a petition if for some reason they deny the surgery.