The baby is not counted as having had health insurance all year. If he did have health insurance, he had it only for the months that he was alive. Part of a month counts as a full month. So if he was born in October he had coverage for October, November, and December. When you go through the Health Insurance section of the interview, you indicate that he had insurance for part of the year, and you indicate which months he was covered. TurboTax will automatically fill out Form 8965 giving him an exemption with code H for the months before he was born, so there will be no penalty for not having coverage. The following is the description for exemption code H in the IRS instructions for Form 8965.
"Member of tax household born, adopted, or died — During 2015 a child was added to your tax household by birth or adoption, or a member of your tax household died during the year, and you can't check the full-year coverage checkbox on your tax return."
However, the rules for claiming the baby as a dependent are different from the rules for health insurance coverage. As xmasbaby0 said, in the Personal Info section, when TurboTax asks you how many months the child lived with you, you have to select "The whole year."
