The name that comes up in public sources for “who was Jana Barrett married to” is Daniel Barrett, a New Zealand–based animation supervisor at Weta Digital.

From an Oscars fashion piece noting Wellington locals attending the Academy Awards, Jana is explicitly described as being married to Daniel Barrett, who was serving as Animation Supervisor on Rise of the Planet of the Apes at the time.

“Jana’s husband, Weta Digital’s Daniel Barrett… was the Animation Supervisor… for Rise of the Planet of the Apes.”

So, based on available online information, Jana Barrett was married to Daniel Barrett.

Information gathered from public forums or data available on the internet and portrayed here.