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| To my knowledge you would get a B permit for the first 5 years, any child born and living in the same household would most probably get a C due to your husbands C status. Your child would have the same rights to education etc. as a Swiss child. It only becomes complicated if you and your husband want to leave the country for more than 2 years with a view to coming back. Then the C permit would expire. If your family are still here when the child reaches full age he/she will be entitled to simplified naturalization.
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Your knowledge is good. Remove the probablies and you have provided the right answer - ie
As an American you would get an EU B permit and your child if born in wedlock would be entitled to the highest privilege in your household ie a C permit. As stated if you left for 2 years the C permit would indeed expire however this would not represent a hurdle as the EU bilateral agreement will then be in full force entitling EU citizens to full free movement within Switzerland and a non-restricted permit.