Yes, and that would be illegal. While discrimination against women is more common, our country's anti-discrimination laws are gender-neutral. Under Title VII of the Civil Rights Act of 1964, it's illegal for employers to discriminate "because of sex," and that includes discrimination in any aspect of employment affecting either men or women.
Recently, banking giant JPMorgan Chase settled a class action over its paid parental leave policy, which the plaintiffs alleged discriminated against fathers.
The case began two years ago when a male Chase employee told the bank that he planned to take the 16 weeks of paid parental leave that were offered to primary caregivers at Chase. According to the lawsuit, he was told that "men, as biological fathers, were primarily not the primary caregiver."
The man filed an EEOC complaint, and Chase immediately offered to give him the full period of leave he requested. However, other men at the bank had presumably also been denied primary caregiver leave despite being primary caregivers.
As a result of the class action settlement, Chase has agreed to pay $5 million to compensate each man who was wrongfully denied the leave. That could be hundreds or even thousands of men.
The man and his lawyer claim that Chase changed its policy in response to the class action. The bank counters that it merely clarified the policy, which was always meant to be gender-neutral. Either way, its' a win for Chase employees.
Do mothers and fathers always have to get the same amount of leave?
Not necessarily, but the reason for any difference cannot rely on stereotypes or otherwise be discriminatory.
First, it's important to note that federal law doesn't require companies to offer paid parental leave. The Family and Medical Leave Act does require 12 weeks annually of job-protected, unpaid, leave for employees who become new parents and for other family and medical purposes.
When paid parental leave is offered as a benefit, however, it must be offered on the same terms to both men and women.
Mothers can be offered additional medical leave, paid or unpaid, to recover from a birth. That would be an example of a gender-based difference in policy that is not discriminatory.
As for the Chase employee who filed the complaint and class action, he has heard from numerous men with similar complaints. He told NPR that he is glad to have brought the case, "so that we could get rid of some of these stereotypes where it's the woman's job to have babies and cook and the man gets back to work and pays the bills. That doesn't work for everyone; it's not the century that we live in."