Peer Support for Veteran Families Act This bill requires the Department of Veterans Affairs (VA) to establish an education program and a peer support program for the education and training of family members and caregivers of eligible veterans with mental health disorders. Under this bill, eligible veterans are those who are enrolled in the VA health care system. Such veterans must give permission for their caregiver or family caregiver to participate in either program established under this bill. The VA must establish a four-year education program to provide a course to family members and caregivers of eligible veterans on matters relating to coping with mental health disorders in veterans. In implementing the program, the VA must enter into contracts with certain nonprofit entities with experience in mental health education. Under the peer support program, the VA must provide peer support to family members and caregivers of eligible veterans on matters relating to coping with mental health disorders in veterans. The VA must provide peer support at each location where the education program is provided, and such support must include regular meetings in group settings between peer support coordinators, family members, and caregivers. The VA must conduct a survey of the satisfaction of individuals who have participated in the education program and the peer support program. VA mental health care providers must monitor the progress of the programs.