Under the federal Family Medical Leave Act (FMLA), you also don't get paid, but your job is held for you. The FMLA applies to companies that have more than 50 employees; you can be entitled to 12 workweeks of unpaid leave during any 12-month period in connection with the birth of a child.
What's unclear though -- and a possible pitfall for you -- is that you refer to yourself as self-employed, but mention that you receive W-2 forms (instead of 1099 forms for independent contractors) from your clients. Are your clients deducting the proper amounts in withholding on your behalf? Look carefully at any agreements you have with your clients (they may treat you as a W-2 employee for tax withholding purposes, but not for the purpose of any other benefits). And speak to your accountant to ensure you're handling your tax situation properly.