If you constantly had some insurance, even if the company changed, your new insurance is required to cover the expenses from your birth. They'll say that they don't have to, and try to get out of it, but you should fight this tooth and nail. I had similar experience with a surgery--my insurance changed, because of a change in employer, between when the condition developed and when the surgery took place. I fought this for MONTHS, but they did eventually pay. All insurance agencies have a "preexisting conditions" clause, but if you were constantly covered by SOME insurance, they still have to pay. Don't take no for an answer. Call the insurance agency, and ask to speak to a supervisor, and then the supervisor's supervisor, until you get someone who actually knows something. Also go through HR at your employer, and have them file a complaint. Finally, if necessary, talk to a lawyer. I ended up sending a big packet of documents certified mail, with a receipt so I could prove that the insurance company received them, containing letters and proof of constant insurance. I also wrote a letter saying that my next step would be a letter from my lawyer (luckily, I have a friend from high school who's a lawyer--he never had to write the letter, but I he would have, if I'd asked). FINALLY, after fighting this for 6-8 mos, the insurance paid.
Health insurance companies will always try to get out of paying things they should. Don't believe them. We had to contest as well when my DD had surgery, and go through HR at my husband's work. The system's a mess, and the insurance companies count on most people giving up before they get what they're entitled to. Keep at it, and if you don't understand something, make folks keep explaining until you do. Read your policy carefully (I know it's terribly boring and confusing!), and be prepared to cite page numbers when you talk to people. It's a pain, but it's worth it--both monetarily for you family, and in the interest of making insurance companies live up to their commitments! GL!