Mental Health Support for Veteran Families and Caregivers Act of 2013 - Requires the Secretary of Veterans Affairs (VA) to: (1) enter into contracts to conduct a 4-year program (with authorization for a 4-year extension) to provide a course of education to family members and caregivers of veterans on matters relating to coping with veterans' mental health disorders; (2) carry out such program in at least 10 VA medical centers, 10 VA clinics, and 10 centers for readjustment counseling and related mental health services for veterans (vet centers); (3) expand such program (within 2 years) to include at least 10 additional medical centers, clinics, and vet centers; and (4) select VA mental health care providers to monitor the progress of the instruction provided under such education program.

Requires the Secretary to: (1) establish a program to provide peer support to family members and caregivers of veterans on matters relating to coping with veterans mental health disorders; (2) provide such peer support, through group meetings conducted at least twice each calendar quarter, at each facility in which the education program is provided; (3) select an individual who has completed the education program to serve as a peer support coordinator for each facility; and (4) select a VA mental health care provider to serve as a mentor to each coordinator.

Directs the Secretary to conduct a survey of the satisfaction of program participants.