The good news: According to Deloitte’s new "Millennial Dad at Work" report, dads are more engaged as caregivers than ever before. In fact, 58 percent of dads are now actively involved in day-to-day parenting and 63 percent of new dads have requested a change in their working pattern. The bad news? Corporate America is lagging behind. Many of the dads who participated in the study reported not having equitable access to the workplace flexibility they need to fulfill their caregiving responsibilities.

The study found that of the 14 percent of millennial fathers who have requested to work away from the office between one and two days per week, only 19 percent are granted access to this arrangement. And of the 40 percent of dads who have requested a change in their schedule, less than half are given the green light. Additionally, only 56 percent of respondents said they believe fathers are treated equally to mothers in the workplace, and 45 percent of fathers have experienced friction from their employers while trying to manage their home and work lives.

Our own research shows that millennial men have the highest demand for PartTime work—at 63 percent—and we speculate that this demand might be indicative of men taking on more of the caregiving and homemaking mantle. Meanwhile, women are taking over as breadwinners, with the Center for American Progress reporting that 43 percent of mothers rank as the sole or primary income earner for their households. And the Bureau of Labor Statistics predicts that women will comprise 48 percent of the workforce by 2050, up from 30 percent in 1950.

"It's clear progress is being made in society and childcare is no longer seen as just the domain of the mother, but employers appear to be slow in catching up," Activ People HR's Adrian Lewis blogs for HR News. "Those that want to recruit and retain the best people will need to rethink this, as it could mean losing out on talent to companies that have more progressive policies on flexible working."

Lewis concludes: "For companies looking to stay ahead of the competition when it comes to recruitment and retention, then implementing flexible working for new dads, as well as the wider workforce can be a big incentive, and in turn lead to happier and more productive employees."