Michelle Duggar resting at home after miscarriage

(CBS) Michelle Duggar is resting at home after she and her husband learned she had miscarried while pregnant with their 20th child.

The couple, who appear with their children on TLC's "19 Kids and Counting," say their doctor could not find the baby's heartbeat during a routine checkup on Thursday.

"Our doctor said it was wise to let this miscarriage happen naturally," the 45-year-old mom told People magazine on Friday. "And so that is what we are going to do."

"I am resting and I have felt good physically, which is strange," she added. She was 19 weeks and one day into her pregnancy when the miscarriage was diagnosed, the magazine reports, while the baby measured at 16 weeks.

Her husband, Jim Bob Duggar, wrote a letter to thank friends and fans for their support.

"On behalf of the whole Duggar Family we would like to thank everyone for their prayers, emails and outpouring of love," he wrote in the note, which was provided to the "Today" show's website. "We discovered during a routine 19-week ultrasound that our 20th child, who was due in April 2012, passed away recently. As our whole family is grieving, we also know that God promises to work all things for good in our lives. We rest in knowing, that even though our child has departed this life that we will one day see each other again in heaven."

"Our prayer is that baby Duggar's passing will help us all realize that this life is short, and our relationship with Jesus is the most important thing," he continued. "He gives us a peace in our hearts as He guides us through whatever we might face."

Michelle Duggar suffered an earlier miscarriage while pregnant with the couple's second child. She was taking birth control pills at the time she got pregnant, and the Duggars have previously said the miscarriage is one reason they no longer use birth control.

"We will name this child and will know that we will see those children again someday in heaven," she told People.

Jim Bob and Michelle Duggar are parents to Joshua, 23 (who is married with two children of his own); twins Jana and John-David, 21; Jill, 20; Jessa, 19; Jinger, 17; Joseph, 16; Josiah, 15; Joy-Anna, 14; twins Jedidiah and Jeremiah, 12; Jason, 11; James, 10; Justin, 8; Jackson, 7; Johanna, 6; Jennifer, 4; Jordyn, 3, and Josie, who was born three-and-half months premature on Dec. 10, 2009.