sandwich generation
n. People who must care for both their children and their parents; people who have finished raising their children and now must take care of their aging parents.
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"The sandwich generation is being chewed on at both ends," Novelli said. The boomer generation is struggling to help support aging parents and pay college tuition for their children.
—Ann McFeatters, “Boomers approaching retirement with angst,” Pittsburgh Post-Gazette, November 20, 2002
They have been called the ''sandwich generation.'' Some are in their 30s or 40s, caught between the needs of their growing children and the needs of their aging parents. Others are in their 50s or 60s - planning for relaxation and travel, their children grown - when they must take on a new guardianship, becoming parents to their parents.

Only now are social agencies beginning to recognize the sometimes desperate need of members of this middle generation for help in coping with the housing, financial, medical and emotional problems of their parents, as well as with their own guilt and resentment.
—Nadine Brozan, “'Sandwich generation' has parents, children to worry about,” The Globe and Mail, May 18, 1978
1975 (earliest)
Middle aged Japanese today are members of a ‘sandwich generation’ in that, like people in middlehood anywhere, they are weighed down by the elders from above, pressed against by insurgent youth from below.
—David W. Plath, “The Last Confucian Sandwich: Becoming Middle Aged,” Journal of Asian and African Studies, January 01, 1975
The phrase The Sandwich Generation ™ is a trademark of Carol Abaya Associates; the trademark refers to "Magazines and newsletters containing articles, stories and information about issues and events of concern to adults who have both children and an aging or elderly parent."