Actually, OPM has issued guidance that says that the 12 weeks provided by FMLA are in addition to any sick or annual leave you have.
http://www.opm.gov/oca/leave/html/fmlachng.pdf (scroll to the part about "stacking" leave)
A lot of people choose to use their sick/annual during FMLA so that they get paid, but you do not have to (my supervisor, for example, is allowing me to take 6 weeks sick and the remainder of my maternity leave without pay so that I can preserve my annual leave to use for when my child gets sick and to travel to see our families during the 2012 holidays). Based on what OPM says, it seems you could use the 6 weeks sick leave to which you are entitled for vaginal birth and then 12 weeks FMLA leave on top of that for a minimum of 18 weeks maternity leave (if you have the sick leave accrued).
The only caveat is that, to the extent you intend to "stack" with annual leave, your supervisor has the discretion to deny your request for annual leave, so if you have an unsympathetic supervisor your ability to stack would be limited to sick leave during the period of post-birth incapacitation.