I am aware of only a few combined family prac/psychiatry residencies. The AOA has four "specialty emphasis" psychiatry rotating internships for PGY-1, and the ACGME (allopathic) search engine of residencies shows no such programs. FREIDA shows a match of 10 such programs.
Check the
FREIDA website for details.
Psychiatry/Family Medicine:
California
1. University of California (Davis) Health System Program
Sacramento, California 720-05-44-004
2. University of California (San Diego) Program
San Diego, California 720-05-44-005
Hawaii
3. Tripler Army Medical Center Program
Honolulu, Hawaii 720-14-44-008
Iowa
4. University of Iowa Hospitals and Clinics Program
Iowa City, Iowa 720-18-44-009
Maryland
5. National Capital Consortium Program
Andrews AFB, Maryland 720-23-44-012
Ohio
6. University of Cincinnati Hospital Group Program
Cincinnati, Ohio 720-38-44-006
7. Case Western Reserve University/University Hospitals of Cleveland Program
Cleveland, Ohio 720-38-44-013
Oklahoma
8. University of Oklahoma College of Medicine-Tulsa Program
Tulsa, Oklahoma 720-39-44-001
West Virginia
9. West Virginia University Program
Morgantown, West Virginia 720-55-44-010
Wisconsin
10. Medical College of Wisconsin Program
Milwaukee, Wisconsin 720-56-44-011