There are three classes of programs:
1) Fully-funded. Tuition waiver and stipend for all years of study. This includes almost all MSTPs, which are PARTIALLY NIH funded through a NIGMS grant. This also includes many MD/PhD programs that are not MSTPs.
That being said, not all spots are fully funded at all MSTPs. Hopkins still takes students that are not fully-funded for example. But, the vast majority are.
2) Partially-funded. Typically these provide tuition waiver for medical school but no stipend OR tuition waiver and stipend for last 2 years of med school but not the first.
3) Unfunded. Almost everyone will give you tuition waiver and stipend for graduate school. Graduate school is mostly free labor on the part of the graduate student, and hence you should be paid. Graduate schools are also happy to get well qualified students, of which medical students typically are. Getting medical school paid for is the hard part.
This comes up a lot, so I'll mention that there is no DO/PhD program that falls into catagory 1. If you are in a catagory 3 program you can try for a F30 grant and a small percentage are able to bump themselves up to catagory 2.