Yes, but it all depends on your leave policy. U.S. Department of Labor (DOL) regulations state that an employer may limit spouses who are both employed by the same employer to a total of 12 weeks of FMLA leave in situations where the leave is for the birth or placement of a child or for caring for a seriously ill parent. This applies even where spouses are located at worksites more than 75 miles away from each other or by two different operating divisions of the same company. The regulations state that if one of the spouses is ineligible for FMLA leave, the other spouse is entitled to the full 12 weeks of leave. However, if the child has a serious health condition, each spouse is entitled to 12 weeks of FMLA leave, even if employed by the same employer.
The regulations also state that if the spouses take less than 12 weeks of FMLA leave for adoption, each spouse can take the difference between 12 weeks and the amount of leave he or she took if it is needed for a serious illness. So, for example, if each spouse takes six weeks of leave and one spouse needs FMLA leave for his or her own serious illness, he or she can take an additional six weeks of FMLA leave for that.
Source: FMLA Reg. Sec. 825.121(a) as reported in the Employee Benefits Management Newsletter, Issue 633, May 2, 2017.