When I quit my job to do a postbac I was worried about the same thing. The school I go to offers quite reasonable health insurance, and it's been way cheaper than COBRA. It looked really cookie cutter, but it's been fine. An annual is covered, there's prescription coverage, mammograms with a deductible, etc. My school offers up to full year coverage, which includes summer whether I'm enrolled or not.
In looking through the MSARs over the last couple years, it looks pretty standard for med schools to offer similar health insurance. This is a good interview answer/question for "do you have any questions for us?" imho.