LONDON — In their first joint appearance since Christmas, senior members of the British royal family waved to the crowds from the Buckingham Palace balcony, as Royal Air Force jets flew past in honor of the king’s official birthday on Saturday.

The British people celebrated their monarch with the usual pomp. But this time was different. King Charles III has cancer. He was not on horseback. And his daughter-in-law Princess Catherine, also undergoing treatment for cancer, was stepping out in public for the first time in six months.

The king, wearing the red uniform of the Irish Guards, rode in a carriage alongside his wife, Queen Camilla, as they made their way through the crowd-lined streets on a rainy June day.

Catherine, in a sleek black-and-white outfit complete with a bow, matching hat and gold brooch, sat in another carriage, accompanied by her three children. Her reappearance in the public eye had been hotly anticipated by the public, and she appeared ready for the scrutiny, picking a window seat, looking through the glass, and smiling and waving.

The Princess of Wales, still popularly known as Kate Middleton, released a deeply personal note Friday about her intention to attend the Trooping the Colour parade.

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“I am making good progress, but as anyone going through chemotherapy will know, there are good days and bad days,” she wrote. “On those bad days you feel weak, tired and you have to give in to your body resting. But on the good days, when you feel stronger, you want to make the most of feeling well.”

Neither Catherine nor King Charles III has revealed what type of cancer they have, nor the details of their treatment.

The king, 75, has returned to public duties since his February diagnosis. He looks good. But his appearances have been limited. He hosted a garden party at Buckingham Palace. He was in France last week to honor the soldiers of D-Day.

Catherine, 42, who underwent abdominal surgery in January and revealed her cancer diagnosis in March, following weeks of intense speculation and even conspiracy theories about her whereabouts, wrote Friday that her treatment will continue “for a few more months.”

“On the days I feel well enough, it is a joy to engage with school life, spend personal time on the things that give me energy and positivity, as well as starting to do a little work from home.”

Her statement was accompanied by a photograph of her standing alone under a weeping willow on the Windsor Estate.

She said she was looking forward to attending the king’s birthday parade with her family and hoped to join “a few public engagements over the summer.”

But she added, “I am not out of the woods yet.”

She wrote, “I am learning how to be patient, especially with uncertainty.”

The annual Trooping the Colour parade is a visual extravaganza, featuring 1,400 parading soldiers, 400 musicians and 242 military horses.

One of the horses in the king’s escort, Tennyson, was among those who galloped through central London after being spooked by construction work in April. Another two, Trojan and Vanquish, are providing ceremonial guard for the royal palaces. The two horses most seriously injured in that episode, Vida and Quaker, are still receiving veterinary care.

The monarch’s birthday ceremonies involve the presentation of regimental flags, called “colours.” The king’s flag is “trooped” or carried through the military ranks, a centuries-old tradition originally designed to impress upon young soldiers which flag to rally around in battle.

The birthday parade is not held on Charles’s actual birthday. That is Nov. 14. But successive monarchs have celebrated their official birthdays in June, maximizing the potential for decent weather.

It being Britain, Saturday’s spectators still ended up drenched in rain, with thunderclaps audible in parts of London during the parade. But that was of little consequence to Britain’s royal fans, who cheered loudly as Charles, Kate and other members of the royal family emerged on the balcony to wave.

Princess Kate and King Charles at the Trooping the Color ceremony

Princess Kate and King Charles III make first joint appearance at king’s parade in London.