While there's no specific law covering discrimination against employees due to family responsibilities, there are laws that may protect you if your employer is big enough.
1. Sick/disabled family membersIf an immediate family member (or you) has a medical condition that requires regular doctor's appointments, you may well be entitled to up to 12 weeks a year of unpaid leave. This leave can be intermittent, which means that you get up to about 60 days a year or 480 hours. (That's a whole lot of doctor's appointments.)
This applies only if you need to miss work for a serious medical condition of a family member, AND your employer has at least 50 employees, AND you've been there at least a year.
If you know you will need this type of leave, make sure that you notify HR in advance so you make sure you're covered. If you think you qualify and they claim you don't, then contact an employment lawyer in your state to discuss your rights.
2. Sex stereotypingThere's no law making sexual stereotyping illegal, but it may fall within sex discrimination if your employer has 15 or more employees. For instance, . . .
Thanks again to Gina Misiroglu of Red Room for putting me in touch with the AOL people!