dennisbbb,
Paternity leave is usually covered by Family and Medical Leave Act of 1993 chiph mentioned. Companies with fewer than 50 employees don't have to give the leave (as they often cannot afford it).
Under FMLA (see chiph's link), an employee who worked for a covered employer for at least 1 year can be allowed "to take job-protected, unpaid leave, or to substitute appropriate paid leave if the employee has earned or accrued it, for up to a total of 12 workweeks in any 12 months because of the birth of a child and to care for the newborn child, because of the placement of a child with the employee for adoption or foster care, because the employee is needed to care for a family member (child, spouse, or parent) with a serious health condition, or because the employee's own serious health condition makes the employee unable to perform the functions of his or her job".
Thus, your employer has the right to request that you take all or part of your paid leave (vacation, personal days, floating holidays, or, in some cases, sick leave) as a part of your leave before taking any unpaid leave. They probably have to notify you in advance of that, I don't remember, so check all the paperwork carefully; you might find that they did say something but you didn't notice. Also read the law (the link again) through.
I took FMLA a few years ago; I was requested - before the actual leave, not after - to take all of my unused paid sick leave first, then most of my unused vacation and other paid leave time, then go unpaid for the rest of my leave. I was able to negotiate to keep 1 week of my paid vacation time for emergencies.