Kate, the Princess of Wales, has completed chemotherapy and will make some public appearances in the coming months, bolstering Britain’s royal family after it was rocked by the twin cancer diagnoses of the princess and King Charles III.

The 42-year-old wife of Prince William released a video Monday in which she appeared alongside her husband and children as she described how difficult the past nine months have been for her family and expressed “relief” at completing her course of treatment.

“Life as you know it can change in an instant, and we have had to find a way to navigate the stormy waters and road unknown,’’ she said in the video, which was shot in a woodland near the family’s summer home in Norfolk. “The cancer journey is complex, scary and unpredictable for everyone, especially those closest to you. With humility, it also brings you face to face with your own vulnerabilities in a way you have never considered before, and with that, a new perspective on everything.”

The royal family has been buffeted by health concerns this year, beginning with the announcement in January that the king would receive treatment for an enlarged prostate and Kate would undergo abdominal surgery. In February, Buckingham Palace announced Charles was receiving treatment for an undisclosed type of cancer. Six weeks later, Kate said she, too, was undergoing treatment for cancer, quieting the relentless speculation about her condition that had circulated on social media since her surgery.

While the announcements triggered an outpouring of good wishes for the ailing royals, they also put the royal family under tremendous pressure. Queen Camilla and Princess Anne, the king’s sister, took on additional duties to cover the seemingly endless list of public events that make up the daily routine of the House of Windsor. William also took time off to support his wife and their three young children.

Charles began his return to public duties in late April when he visited a cancer treatment center in London. He is scheduled to make the first long-haul trip since his diagnosis when he travels to Australia and Samoa in the fall.

Kate said Monday that while she had completed her chemotherapy treatment, the path to full recovery would be long and she would “take each day as it comes.”

“William and I are so grateful for the support we have received and have drawn great strength from all those who are helping us at this time,” she said. “Everyone’s kindness, empathy and compassion has been truly humbling.”

In June, the princess acknowledged that she had good days and bad days while undergoing treatment.

While she stepped away from most public duties during her treatment, Kate has made two appearances this year. First, during the king’s birthday parade in June, known as Trooping the Colour, and most recently during the men’s final at Wimbledon in July, where she received a standing ovation.

“To all those who are continuing their own cancer journey — I remain with you, side by side, hand in hand,” Kate said Monday.

“Out of darkness, can come light, so let that light shine bright.”