Women Veterans and Families Health Services Act of 2019 This bill addresses fertility treatments, counseling, and other health-related programs for veterans and members of the Armed Forces. Specifically, the bill requires the Department of Defense (DOD) and the Department of Veterans Affairs (VA) to provide fertility treatments and counseling to covered veterans and active duty servicemembers or a spouse, partner, or gestational surrogate of such veteran or servicemember. A covered veteran or service member is a severely wounded, ill, or injured former or current member of the Armed Forces who has an infertility condition incurred or aggravated while serving on active duty. DOD must establish procedures related to gamete retrieval and storage. Fertility counseling and treatment are included within authorized VA medical services. The VA may pay the adoption expenses (for up to three adoptions) for a covered member who is enrolled in the VA health care system. The VA must facilitate specified reproduction and infertility research conducted collaboratively by DOD and the Department of Health and Human Services. The VA shall enhance the capabilities of the VA women veterans contact center to respond to assistance requests and refer such veterans to federal or community resources. The bill permanently extends and expands a VA pilot program related to group reintegration and readjustment services for certain women veterans. The bill provides child care assistance to qualified veterans receiving (1) mental health care services or intensive health care services, and (2) readjustment counseling and related mental health services.