From EDD:
For California workers covered by State Disability Insurance, Paid Family Leave (PFL) insurance provides up to six weeks of benefits for individuals who must take time off to care for a seriously ill child, spouse, parent, or registered domestic partner, or to bond with a new child.
I learned about this as I did my taxes this year. Had I done my 2009 taxes by myself I may have learned of this, and taken advantage of this. If/when we have a second child I plan on taking advantage of this.