How do I handle the 1095 form if my parents paid for my health insurance, but are not claiming me as a dependent on their income taxes?

You will need to enter it on your return, then select I share this policy with another taxpayer. Then you will be able to allocate an amount to you and your parents.  You can claim 0% or 100%, they can do the same as long as it adds up to 100%. Many times parents paid the premiums and will allocate the full amount to themselves, while the kids just enter the form and allocate 0%.  Just check with your parents to see how much they claimed for themselves.