Due to the coronavirus pandemic, the stars — who tied the knot for the second time in August 2019 on a yacht in Capri, Italy — have been spending all their time together at home.
"All I can say is I picked the right person, hallelujah. He's amazing," Klum, 46, tells PEOPLE.
"So far, it's been amazing. I picked the right person. It's a different kind of living right now because normally you see work people more than your own family and now the roles have reversed. It's good," she raves.
In March, Klum fell ill on the set of America's Got Talent and self-quarantined along with the Tokio Hotel musician, who also got sick. The pair got tested for the coronavirus, and their results were negative.
After recovering, Klum filmed remote episodes of AGT over video conference with her fellow judges Sofia Vergara, Simon Cowell and Howie Mandel, along with host Terry Crews. In one of the videos, which have been shared on the show's YouTube channel, Kaulitz made a brief cameo as his wife was filming in their bedroom.
In addition, Klum has been at home with her daughters Leni, 16, and Lou Sulola, 10, as well as sons Johan Riley Fyodor Taiwo, 13, and Henry Günther Ademola Dashtu, 14.
"It's a learning curve. I can't say that I'm 100% adjusted," Klum says of her at-home schedule and getting used to staying indoors. "It's definitely all a strange feeling every day when you wake up, but I think we're all dealing with it. I've been at home with my family cooking, cleaning, and there's a lot to do."
"The kids are all being homeschooled," she says, adding that the first week of learning over Zoom was "difficult to figure out because no one did a course for anything like that, including the teachers and the schools."
"It was a learning curve for them, for us, for everyone. But after the first week, we all got a hang of it and we're doing what we're supposed to do," Klum shares.
Along with spending quality time with her husband, the Making the Cut co-host says the silver lining of the pandemic has been bonding with her kids.
"For me, it was really putting my work hat on the hanger for a while and really just have my mom hat on, which is beautiful," she shares. "I normally don't get to do as many things as I do now, because obviously, I don't have anyone to help me with things right now. So, all the mom duties are more a priority right now."
While filming her Amazon fashion show took her around the world, and many other projects took time away from her family, Klum has been focused on her loved ones.
"Normally when I go to work, there is more that you see your family in the morning and you see them at the end of the day. And now, it's all day, which is the one amazing thing during all of this because it's nice to be with your family all the time," she says.
Season 15 of America's Got Talent premieres Tuesday at 8 p.m. ET on NBC.