I am also at BU (staff) and my wife and I had our first child this past spring. Our benefits are good compared to my past employers, and I took a few weeks of paid vacation time so I could stay home with my wife and help after her c-section. I'm glad to hear that there is leave available for graduate students as well. Are the 60 days of paid leave for sick time or paternity leave? I had not heard that anything changed recently with the rules around time off.
The 60 days are specified as paid paternity or maternity leave[1]. I don't actually know what the sick leave policy is. As a graduate student your schedule is flexible. I am not taking classes, but I can work as much as I want, and as long as the vacations are reasonable they aren't really tracked. I think that goes along with officially being paid for 39 hours a week with the expectation that you are there much more.
Best of luck to you and your wife!