An EOB is an Explanation of Benefits. It explains everything for that specific claim of services. Depending on the insurance company, they are sent with every claim submitted and adjudicated but some insurance companies (and states) don't require the subscriber to have one unless asked.
I would ask for one to see where the problem is. It is like driving blind, not knowing what was submitted and what the insurance company will pay and what the doctors will eat in losses.
See if the hosiptial has a patient advocate, they do pretty good work (if they are any good) in sorting out billing messes. But don't pay until they resubmit the claim.
By the way the one fallacy with this entire health care 'reform' is that the doctors know what's going on with the patients and the insurance companies but that is farthest from the truth. Very few doctors do their own billing, and those who do are very selective about who's insurance they accept. Those who don't, which I think maybe in the neighborhood of 97% hand that off to office staff or outsourced. The one thing that I am really frustrated with any "health care reform" is having the doctors involved with it - they are not the people having the problems.