Welcome to the site, I take it your husband is a reservist. They should put him on incap orders. Your husband is entitled to recieve medical care through the VA for five years once he comes off of orders. By going to the VA he could actually help himself if he should be MEB'd. If it were my husband, I would take him to the VA right away. You'll need to build a case for the military, and the VA. I would start by gathering as much evidence as you possibly can. His demob papers that indicate it happened in Iraq, statements from battle buddies who say him get hurt, or complain. The VA uses a more probable than not criterea. So you don't HAVE to have a LOD to get service connected with him. If you can get them to service connected, he can force the issue with his unit on getting a LOD. You HAVE to have it as a reservist to get it rated should he be MEB'd. If your husband is MEB'd and found unfit, they won't pay him without it.
So for the VA there are two sides of the house. There is the medical care he will recieve and there is the Compensation and Pension. The two don't meet, and don't know what the other is doing.
He will need to seek treatment there, he will need his DD214 from deployment, and then put in for compensation and pension. It is highly recommended to use a Veteran Service Officer, there are three approved by the VA, DAV, VFW, and the Military Order of the Purple Heart. Your husband will need his VA record to state his diagnosis, and need for surgery so take all his docs from the doc he see's now.
My husband tore his shoulder all to heck too, and I know it's a long painfull recovery. You need to get it service connected, and rated by comp and pension. When he gets the surgery, while he cannot work, the VA will pay him 100%. You'll need a statement from the doc saying his recovery will take so long, and that he cannot perform his normal work while recovering. My husband was a mechanic during his, and is right handed so couldn't perform his normal duties, you can go on Department of Labor, and download the description of his job, a statement from his employer saying what his job/job requirements are and submit it with the form they require ( I don't remember the form number) with his request for comp and pension.
I know this isn't an easy answer and getting a rating is a long wait In my husbands case his surgery was needed to fix the tear (it was major) but delaying it didn't cause more damage.
Outside of that, someone with better knowledge of the workings of the military would have to respond. You could contact any of the moderators, or Jason the site administrater they are all wonderful, and so much better with answers than me.
I wish you luck, keep us posted