Research for Britain's Twins and Multiple Births Association (TAMBA) found that 62 % of those asked said they were financially worse off after their babies were born, compared with 40 % of other parents.
In all, 28 % of parents of twins or triplets separated or divorced, compared with 24 % of other families.
Families with twins or triplets reported higher levels of material deprivation and were more likely to be unable to afford key items for their children.
"We love our twin boys dearly, but have spent much of the last two years sick with worry, just trying to give them the basics," mother of twins Suzanne Pammen said in a statement released with the results of the survey.
Nine months after giving birth, mothers who had had multiple births were nearly 20 % less likely to have returned to work than mothers of singletons.
"The report found that twins and triplets are more likely to be born to married and older couples, who are in paid employment," said Professor Stephen McKay of the University of Birmingham, who conducted the research on behalf of TAMBA.
"It is deeply concerning that twins or triplets are experiencing greater levels of material deprivation than singletons, and that their families are at greater risk of separation and divorce," he added.
The report analysed the datasets of The Millennium Cohort Study, which tracked a group of 18,500 children born in 2000/2001, and the annual Family Resources Survey, the British government's key source of statistics on poverty and low income.