A mortgage loan is a secured loan--it involves a promissory note and then also a security interest in a property being mortgaged. So a mortgage loan wouldn't work for someone who is looking to finance med school. In theory you could do a cash back refinance or mortgage loan which would put some cash in your pocket. It wouldn't be enough to pay for medical school, but they were very common before the housing meltdown (not so common now, for obvious reasons). If you already own a property that is paid off or has significant equity, you might be able to do a second mortgage/home equity loan. Remember that any loan proceeds would be secured by your property or home, and if you default, you lose your house. Also, second mortgage rates are typically higher than first mortgage rates because of the increased risk involved. I have no idea if those rates would beat student loan rates.
My guess is you would find it very difficult to find any bank that would finance a medical education outside of the typical student loan sphere without significant security. However, I haven't explored that. Unsecured loans carry the most risk and therefore carry higher rates. That's part of the reason why student loans are generally nondischargeable in bankruptcy court.