Derek is receiving 24-hour-care at home, which Kate has adapted for his needs.
Susanna opened the show by saying it was “incredible” to be presenting with Kate.
Revealing Derek returned home from hospital on Wednesday evening, Kate said: “It’s extraordinary. We are over the moon and overwhelmed.
“It’s like when you first bring home your first born home and you’ve been planning for nine months.”
Susanna said it must benefit Derek being surrounded by Kate and his children Darcey and William again.
“It was a medical reason for coming home as well as our desire and his desire too, to try and encourage a more normal environment to stimulate his recovery, cognition, and consciousness better.”
She added that their children have been “loving” having their dad home – after going six months without seeing him.
“They are excited and overwhelmed,” she said.
Kate explained that while Derek is at home they have an alarm system in place for him to call if he needs something and 24 hour care staff living with them.
“If you are wondering why I’m here – there are people there,” she explained. “Someone is there for Derek and the children so we’re all good.
“We gradually need to make everything work.
“We’ve had a couple of lovely moments where [Derek] has reacted to something Darcey said.
“I don’t want to get my hopes up too much.”
During an emotional interview on Friday’s Good Morning Britain, Kate described the moment Derek arrived home.
“As we came home I could see two little faces of [the couple’s children] Darcey and Billy at the window and they sort of ran to the door and he immediately burst into tears and there was a lot of hugging,” Kate said.
“We got him inside and he absolutely knew he was home. He is responding all the time. What he’s not able to do is talk and say ‘why the hell is the place such a mess?’ It’s not like that but he is absolutely responding and aware.”
Good Morning Britain airs weekdays at 6am on ITV.