Is it normal to have separate cards for separate costs???

Back in May I had surgery and everything went fine. A couple weeks ago I was looking over the coming bills from the hospital and the claims listed by my insurance company. The hospital listed 4 separate things for the surgery, but the insurance only had one of those items listed as a claim (the anesthesia). I called the company to ask about why they only showed one item. The agent said that they had no record of any other items listed for that day. She even commented that it was weird that they only listed the anesthesia but no surgery. I called the hospital and they said that they did send the records of those items to the insurance so that it’s on them to pay for it.

I’m worried that the insurance is trying to get the full cost of the surgery pinned on me. Is there anything I can/should do about this?

UPDATE:

The claims finally got processed by my insurance so what I have to pay is much more manageable. I don’t know if me talking to them helped or not, but considering the timing it might have.

Thanks for the help and info everyone.