EAP works differently with each one. It's an "additional" benefit. One pointer for ALL EAP's is to make absolutely certain you keep a separate file for EAP visits, the reasoning behind it is that it's a complete and separate benefit employers give employees and is STRICTLY confidential. Even the Major Med carrier will not be able to give you information on EAP's, eligibility, etc because one does not know about the other. 99% of the time there are no copay's or coinsurance. EAP's usually have a max per incident OR per patient/annually. Again, they are all different, best to get the guidelines for filing and authorizations via the EAP carrier.
