If a Canadian living in the U.S and married to an American has a child in Canada can the child be both an American and Canadian citizen?

Yes, they can and are. Canada will recognize the child naturally because they were born on Canadian soil, and to a Canadian parent. The child will also inherit the US Citizenship of the American Parent, although the Parent will have to declare the child to the U.S. Consulate showing their proof of citizenship as well as the child's Canadian birth certificate.