I worked with AES to defer mine with both pregnancies. There are several different options. Unless you make interest-only payments during the deferment, your monthly payments will go up when you resume paying to account for the interest that accrued during your deferment. Mine went up maybe $15 or $20 a month.
Also something I learned recently, if you're on an income based repayment plan, your monthly payment will be reduced with a child, even being pregnant with your first counts. My payment went down drastically when they added my soon to be dependent.
I've put my private loans in forbearance before. Payments stop for a few moths, but interest still keeps coming. Make sure to chat specifics with your lender!
I just put my loans on forbearance as my maternity leave is unpaid. Most companies offer you up to 36 months of forbearance. You can apply online or over the phone. It takes just minutes and it's very easy. Just remember you will still be accruing interest.
Re: Student loans during maternity leave