If you want to get the best out of your health plan, you will have to understand how it works, what rights you have under the plan and how to register a complain if you are dissatisfied with the care you are receiving, whether from the company, or from your doctor. It is your right to receive test reports both for yourself and for your family members. If you are enrolled under a managed care plan, you can ask for your doctor to be changed if you are dissatisfied with him. You can shift to a different plan or a different company altogether, if you are dissatisfied with what you are receiving.
Most plans have a well set out way in which you can complain against any decisions or authorization your plan provides. If your company refuses any of your claims, you can file an appeal against it through the appropriate appeal process. Most of your differences will be resolved at this stage only, and you will only need to go for a legal process very rarely.
Make sure you keep records of all communications you have had with the company. Also keep copies of claims and bills. It might also be a good idea to maintain a record of people you have talked to, their names and time, date of the conversation.
If you are still dissatisfied with the process, you can approach the state insurance department on the right way to proceed.