The National Institute of General Medical Science (NIGMS) supports combined MD/PhD programs through the Medical Scientist Training Program (MSTP). The MSTP provides funding to support MD/PhD programs at 41 U.S. medical schools, which can be found here.
These schools have NIH funded MD/PhD MSTP programs which cover tuition for both medical school and graduate school, as well as provide the student with a stipend. Not all MD/PhD programs are fully funded. Information about the MSTP may be obtained by contacting the institutions linked above or the MSTP Program director, Bert Shapiro, Ph.D., at the following e-mail address shapirob@nigms.nih.gov.
It is important to note that acceptance to MSTP programs is very competitive, moreso than just applying to medical school for an MD program. The Admissions Committees are looking for you to have significant undergraduate research experience and demonstrate your commitment to a career in biomedical research. Accepted students usually have more than a year of in depth, independent experience in research and are U.S. citizens or hold Permanent Resident Visas.