If you are able to Itemize your deductions, you can add medical premiums (for Medical and hospital insurance, not all insurance) paid with after tax dollars to Medical Expenses, which will appear on Schedule A (Itemized Deductions). For most versions of TurboTax, this appears under Deductions & Credits.

Note that your medical expenses must exceed a 10% of your AGI (7.5% if either of you are 65 or older or anyone in tax years 2018 and 2019), so, unfortunately, many taxpayers do not get any benefit from trying to deduct medical expenses. But if you have a low AGI or a lot of other unreimbursed medical expenses, it may be worth it.

[Edited 4/2/2020 3:41 pm CDT - updated for 2019]