The rumor that the couple had split came shortly after Hamm, 44, credited Westfeldt, 45, for helping him overcome an addiction to alcohol, for which he completed 30 days of treatment earlier this year.
"The story that appeared in this week's edition of In Touch magazine is not true," the couple's rep said in a statement to PEOPLE. "The only gentleman Jennifer visited regularly in Connecticut was Jon, while he was in rehab. They continue to ask for the public's understanding and sensitivity during this challenging time."
"He needs [Jennifer]," a source told PEOPLE of the stability Westfeldt brought to the Mad Men star's life. "He has to have that in his life."
Westfeldt acknowledged in an April cover story for GQ that "the darkness of Don [Draper] has weighed heavily on Jon."
In December, Hamm delivered a touching tribute to Westfeldt at the PEOPLE Magazine Awards: "There's another person who's actually sitting in the audience who basically told me when I wasn't working that I was still talented," he said. "And she's stuck with me for the last 16 years, even if the talent question remains up for grabs."
Westfeldt – who wrote the films Kissing Jessica Stein and Friends with Kids, which she also directed – cast Hamm in her projects when possible and was a steady presence by his side as he was nominated for seven Primetime Emmys for his leading role on Mad Men.
Reporting by JULIE JORDAN