As others have pointed out, post-tax dollars are what you'll use. Just as a quick note, as you'll be using
post-tax dollars; in the past, I've refused to take contractor plans because they almost always are inferior to what I've been able to get off the private exchange ehealthinsurance. A few people have written excellent articles on Get Rich Slowly here and here about them in detail if you want more information.
Generally, contractors (and sometimes employees) are offered a few plans (3-4), and this health exchange gives you a little more freedom to pick your plan, which in your situation may help. It isn't always cheaper, but depending on your needs, you may obtain a better deal.
Forgot to add this: this option has also made switching jobs easy as well since I don't have to pay COBRA. While it depends on the situation, this can sometimes come out significantly cheaper. For instance, if I were to take the employer health plan next year, I would lose ~$450 a month, whereas the private exchange option is ~$300. But, if I were to switch jobs, decide to opt for self-employment, or a layoff, the COBRA would be even higher than ~$450.