02/28/2012 at 04:00 PM EST
Ethan Zohn isn't one to back down from a challenge. Currently battling
a recurrence of his Hodgkin's lymphoma
, the former Survivor
winner underwent a stem-cell transplant Wednesday from one of his brothers – and he had a particular condition for his doctor.
"Ethan asked the doctor what was the record time for getting out of here, so he wants to beat that," Zohn's longtime girlfriend Jenna Morasca, who is staying with him at the hospital, tells PEOPLE.
"His doctor said there was no prize, and Ethan said, 'Yes, there is. You're going to tell the other patients that I made it out in three weeks.' "
Returning to the same ward where they stayed two years ago when Zohn was first diagnosed was difficult for the couple.
"No one wants to come back here. Even though the nurses and doctors are wonderful, this is one place where you really don't want to see anybody ever again," Morasca says. "Then starting the chemo and being attached to a pump that you're going to be attached to for the next three to five weeks made it very real."
On a happier note, Morasca says the support they've received from around the world has made all the difference. With help from family and friends, she was able to duck out of the hospital [Monday] to shoot the first episode of her new show, Fitness Guinea Pigs
, which will air on YouTube's news channel.
And though Zohn's immune system is weakened, he can routinely have healthy visitors to his room, which he refers to as his "bubble." The two even created the Twitter account @Ethansbubble
, which their friends can access to pen comical perspectives on the experience.
"We don't know who is actually writing the Tweets, so it makes it really fun," says Morasca. "It's all about thinking positively."
After the transplant, doctors will watch to make sure Zohn's body accepts the new stem-cells before releasing him from the hospital. Until then, the couple is making the best of their close quarters.
"I actually really like it, because he can't escape me," says Morasca with a laugh. "He's forced to be around me all the time and listen to everything I say. I'm like, 'What do you think of this hair?' and 'What about this lipstick color?' And he's over there pressing the pain medication pump button."