FORTUNE — For generations, the division of labor was clear-cut. Fathers were breadwinners, mothers were chiefly in charge of the children, and if anyone had to leave work to take Junior to a doctor’s appointment or attend a parent-teacher conference, it wasn’t likely to be Dad.

Times change. A nationwide survey in late May found that more than half (56%) of employed fathers say they frequently take time off for child-related tasks –markedly more than the 40% of mothers who report doing likewise.

Employers haven’t quite caught on yet, it seems. About two-thirds (68%) of dads with jobs say they’ve experienced “negativity or problems” with bosses over conflicts between work and children. Of those, 57% say this has happened “multiple times.”

“The American workforce is different than it was even five years ago,” observes Dean Debnam, CEO of Workplace Options, an employee training consultancy based in Raleigh, N.C., which conducted the poll.

For one thing, he notes, the Census Bureau counts 2.3 million U.S. households where fathers are raising kids alone. Added to the majority of families where both parents work full-time, “the pressure for fathers to succeed both as professionals and as parents is greater than ever.”

Nor is this shift confined to the U.S. A global study on men and work-life balance in February, cosponsored by Workplace Options and WFD Consulting, found that “finding time to spend with family” was the top concern voiced by fathers in almost every developed nation.

As dads and moms know firsthand — and most employers accept with some reluctance — kids’ needs are not always predictable in advance. Increasingly, fathers are making tough choices that their own fathers rarely faced. Being a parent “doesn’t happen on a set schedule,” observes Debnam, adding that combining hands-on fatherhood with a career “takes creativity.”

Debnam should know: He has five kids himself.

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