Her husband, Paul Ahn, who jokingly refers to himself as a moula, or male-doula, said he was still grieving that he would miss the birth experience.

“I completely understand the policy and it makes sense,” he said. “As a dad and partner, there’s not much I could do to support my wife in the pregnancy process, and being there in labor is one of the few things that I could do, and I guess I’m just sad that I’m not able to do it.”

Bailey Nolan, 34, is having a baby girl in July and was planning to give birth at Brooklyn Methodist Hospital, part of the NewYork-Presbyterian Hospital network. She said she spent all of Monday on the phone with family members and insurance providers trying to figure out what to do.

Her plan is to drive to Philadelphia, where she has a cousin who is an obstetrician. When she is ready to deliver, they will go to the emergency room there. She said a representative for her insurance company told her that it would be difficult to switch providers and suggested this was her best option.

“I haven’t had the best experience in hospitals, and I am not going to deliver alone,” she said. “If something happens, if there is some kind of emergency, I need someone who knows me to help make decisions in a time of stress.”

She believes it is irresponsible to put women in this position.

“It is not the 1950s, you can’t just expect them to go in and sedate them and push out a baby, and then they come home and dad is there smoking a cigar,” she said. “That is not our reality anymore.”

Jesse Pournaras, a doula based in New York City, created a petition asking Gov. Andrew M. Cuomo to review the no-partners policy. The petition has received more than 200,000 signatures since it was launched.