Serena Williams poses with baby for ‘VOGUE’ cover and opens up about dealing with postpartum issues

Days after Serena Williams revealed the harrowing medical scare she went through upon giving birth to her daughter Alexis Olympia, the tennis star's husband took to Instagram to talk about how the ordeal sparked personal fears and strengthened his view of the need for all new parents to get paid leave.

Williams told Vogue earlier this week that back in September when the baby was born via emergency cesarean section, she underwent multiple operations after sustaining a pulmonary embolism.

She said her heart rate had dropped dangerously low during contractions and that the day after her daughter's birth, she became short of breath and doctors eventually spotted several small blood clots in her lungs. Williams later returned to surgery when her C-section wound popped open and after doctors found a hematoma.

Following her surgeries, she was forced to spend her first six weeks of motherhood unable to get out of bed.

Ohanian also told Vogue earlier this week that he thought Williams' health complications made her first few months of motherhood "even harder."

"On top of everything she was going through, the feeling of not being able to help made it even harder," Ohanian told Vogue of his wife. "Consider for a moment that your body is one of the greatest things on this planet, and you’re trapped in it.”

In that same interview, Williams joked about her new daughter, "We're not spending a day apart until she's eighteen."

ABC News' Catherine Thorbecke contributed to this report