While he battles throat cancer, Douglas's 10 and 7-year-old support him with mom Catherine Zeta-Jones

As Michael Douglas battled fatigue and pain throughout his treatment for throat cancer, and in the weeks afterward, the actor and his wife Catherine Zeta-Jones marveled at how their kids handled their dad’s illness.

“Dylan and Carys have been so amazing and supportive throughout all of this,” Douglas, 66, tells PEOPLE of his young children.

Douglas, who stepped out in N.Y.C. Tuesday night for a Variety awards-season screening of Wall Street: Money Never Sleeps and told reporters “I feel good,” is beginning to regain his strength after undergoing radiation and chemotherapy.

A friend adds that he has also leaned on his wife of 10 years: “[Catherine] is a strong woman and very practical. There’s no two ways about it – that’s the Welsh in her. Neither one of them are people who would wallow; they just deal with what has to be done.”

For much more on Douglas’s recovery, pick up this week’s issue of PEOPLE, on newsstands Friday