LIZ JONES: How the past few days have shown us the depth of Kate and Charles’s special relationship – and the very touching thing he said to her after she revealed her cancer diagnosis

It’s the ultimate ‘special relationship’ since Kate became part of the royal family – exactly 13 years ago on Monday.

We’ve seen the reassuring look here and there, the warm smile and loving greetings, a name check and a wink in formal speeches.

But this week, King Charles’ high regard for his daughter-in-law – the one who lives on this side of the Atlantic – received a very public seal of approval.

On Tuesday, Charles admitted Kate to the Order of the Companions of Honor, making history.

The Princess of Wales is the first member of the Royal Family to belong to this select group since the organization was founded by King George V in 1917.

She is in good company. Its 65 members, drawn from the arts, science and medicine, include JK Rowling, Dame Maggie Smith, Sir Paul McCartney, Sir David Attenborough and Elton John.

Wow!

Kate is herself a keen amateur photographer and patron of the Royal Photographic Society, the National Portrait Gallery and the Victoria and Albert Museum.

But this honor is a reward for something more than her efforts in the field of art: it is about the high regard the king holds for our future queen.

We saw a hint of the tenderness between them during last fall’s state visit to Kenya, when Charles called Kate his “beloved daughter-in-law.”

This year came the shocking discovery that both the king and the princess had to undergo treatment for cancer.

They were partners in adversity and found themselves in the same hospital, the London Clinic in Marylebone, with reports suggesting that the king had ‘waddled’ from his room to hers in his dressing gown to make sure everything was ‘okay’ used to be.

It’s no surprise then that they are said to have become closer than ever.

The king invited Kate to lunch in Windsor last month, the day after she recorded the moving video message to the nation revealing her cancer diagnosis.

Charles told his daughter-in-law he was “proud” of her bravery, according to The Times.

Such an intimate, reassuring moment would certainly have helped her deal with her understandable anxiety about the next day’s broadcast.

I imagine that Welsh homes are currently filled to the brim with cards and flowers from well-wishers, so the King must have been racking his brains to come up with a different kind of gesture.

This honor is a smart and intuitive choice.

It’s something that will inspire Kate for the future and the work she can do in an area that matters to her: supporting aspiring photographers everywhere, in war zones, in fashion, in the news.

And it also shows us what a gift she already has, and in spades: the love and support of a generous, understanding father-in-law.

What could be better than that close but non-judgmental, no-pressure friendship as Kate recovers from the past few months of illness and stress?

Of course, she has a father and a brother, as well as a loving husband in William. But these three men are, in a way, too close.

As a born caregiver, Kate will have spent the past few months trying to shield them from her darkest fears by wanting to protect them.

It’s different with Karel. He’s not aloof, but he can certainly be pragmatic. He is also someone who is also going through the experience of cancer.

There’s an easy, humorous rapport, which helps. Yes, they will have shared their fears and their experiences in the hospital, but both are outward-looking.

Let’s not forget that the King is a fountain of wisdom on all things ‘Prince of Wales’, offering insight into how to soothe and reassure her husband, ease his mind and help him unwind.

Kate, in turn, is a kind of conduit between two men who can both be stubborn.

The whole family should be grateful for her steely stoicism about Megxit – and her shrewd diplomacy.

It is said that Kate even played a role in ensuring that ‘Memories may vary’ – a brilliant feat – was included in the Queen’s response to Meghan’s interview with Oprah.

Charles can rest assured that his daughter-in-law, as queen, will handle any future conflicts with aplomb.

And at the root of it all is Kate’s immense respect for the man she calls Grandpa, the man for whom she reportedly reserves her deepest bows.

Maybe she is the daughter he wishes he had.

Kate has never been a prickly princess. She has no hard edges or grudges, so she is easy to get along with. That easy, sensitive interaction with her children seems to have disappeared, making Charles soft and tactile towards his grandchildren.

I wonder if he wishes he was closer to Harry and Meghan’s children, thousands of miles away in California.

A cancer diagnosis certainly puts bickering into perspective.

And that also applies to the love and respect between King Charles and his daughter-in-law, which we have seen recognized in recent days.

I imagine Kate is beaming from ear to ear, excited to get back to work, hang in there and pay back the credit.

What a boost!