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.
Hope this helps