Monse Delgado grabbed the hefty cardboard box of diapers and hugged it close to her chest while her toddler played at her feet. The box held 108 diapers, but it actually contained much more than that.

That box held freedom — from hunger, from fear of infection and from being tied down at home.

Because of the $30 or so she saved with the box she got at the Diaper Bank on Otis Street, Delgado won’t have to choose between buying food or putting a clean diaper on 1-year-old Joe over the next couple of weeks. She will be able to go to school, leaving Joe and his necessary day’s supply of diapers at day care or with relatives. She’ll know her son is swaddled up healthy and clean all day, all night.

“You wouldn’t believe what a difference this one box makes,” Delgado, 19, said with a happy sigh.

As of November, because of a $2.5 million state grant to the San Francisco Diaper Bank, thousands of other parents like Delgado will be able find the same freedom.

The grant makes families who receive CalFresh food assistance — or food stamps — eligible to get free diapers worth up to $100 a month for children under the age of 3. The program will help over 1,500 children.

And because the diapers are distributed through the Diaper Bank, which is run jointly by the Human Services Agency and the Help a Mother Out diaper-aid nonprofit, that makes San Francisco the first county in the United States to supply free diapers to people getting food stamps.

“There have been times when I had to buy diapers instead of dinner,” Delgado said. “I need at least two boxes a month, and that may not seem like a lot of cost to some people (about $30 a box), but sometimes we just don’t have the money. This really helps a lot.”

The expansion to food stamp recipients has been a longtime wish of Help a Mother Out’s co-founder, Lisa Truong. Her statewide nonprofit, founded in 2009, teamed up with the Human Services Agency four years ago to make San Francisco the first county to pay for diapers for the babies of families on state welfare, and she has been on a mission to extend the service ever since.

Some low-income parents can be so cash-strapped they run out of diapers and have to use plastic bags and paper towels. Or they just stay with the child and spend all day cleaning up messes. It can become desperate.

“This is a basic human need, something every baby needs, and no parent should have to choose between a clean diaper for your baby and rent, transportation or food,” Truong said. “If you want to go to work, want your child in day care, or simply want to be able to go outside the house sometimes, you need to have diapers to take with you or to leave with the people taking care of your baby.”

Help a Mother Out’s three dozen outlets in the state, mostly in the Bay Area, handed out their 11 millionth diaper in October, Truong said. She hopes San Francisco’s expansion pushes that number higher — and so far, that’s happening.

“I was giving out diapers to 10 families a day before this expansion to CalFresh, and now it’s doubled to 20,” said Marcella Araujo, who was staffing the Diaper Bank station in the Human Services Agency building on Otis Street when Delgado came in the other day. “Sometimes I’ve had families come in and when they find out for some reason they can’t get diapers, they just leave. Now a lot of them won’t have to.”

Ileana Montano, 39, brought in her 3-year-old, Camilla, and said the free pull-up diapers she gets help make it possible for her to study at community college to be a social worker.

“I don’t think most people understand how important this is,” she said. “I want Camilla to be healthy — there are infections and rashes she can get unless she has clean diapers. And with the diapers I get here, I don’t have to worry about that. I don’t have to worry about paying for them instead of for something else.

“I know so many people who only get food stamps, and who need this kind of service because they can’t afford diapers,” she said. “This is going to help a lot.”

Kevin Fagan is a San Francisco Chronicle staff writer. Email: kfagan@sfchronicle.com Twitter: @KevinChron