Justin Timberlake and Jessica Biel Hold Hands in New York City Following Scandal with Costar

Justin Timberlake and Jessica Biel are out and about in NYC.

Two months after the singer, 38, was seen holding hands and mingling closely with Alisha Wainwright, his costar on the upcoming film Palmer, in New Orleans, the couple were photographed holding hands as they stepped out for coffee in New York City’s Tribeca neighborhood (where they own an apartment) on Jan. 19.

“Justin and Jessica went for a stroll around their neighborhood,” a source tells PEOPLE. “It was chilly, but they looked cozy arm-in-arm. They were both in a great mood, smiling and chatting.”

According to the source, Biel, 37, brought their 4-year-old son, Silas, to N.Y.C. to visit Timberlake for the long holiday weekend since he had off from school on Martin Luther King Jr. Day.

“They are all staying at their Tribeca apartment,” the source says.

For the first time since the scandal, Timberlake and Biel were photographed earlier this month having an intimate dinner at Los Angeles’ Hotel Bel Air, where another source says they spent a four-night long staycation with Silas.

Last month, Timberlake issued a public apology on his Instagram account to apologize to Biel — whom he married in 2012 — after news of his sighting with Wainwright, 30, made headlines.

“A few weeks ago I displayed a strong lapse in judgment — but let me be clear — nothing happened between me and my costar. I drank way too much that night and I regret my behavior. I should have known better,” he wrote in his apology.

“This is not the example I want to set for my son,” he added. “I apologize to my amazing wife and family for putting them through such an embarrassing situation, and I am focused on being the best husband and father I can be. This was not that.”

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Wainwright, 30, whose representative has previously told PEOPLE that there is “no validity” to the romance rumors, returned to work on the Palmer set alongside Timberlake shortly after the scandal.

“Nothing has changed or been influenced by the press reports,” a source close to the set said. “The show goes on.”

A source previously told PEOPLE that Timberlake and Biel would find a way to “work through” the situation.

“It was good that he apologized publicly but obviously the real work he is doing is in private, and hopefully this was just a bad drunken night of this type of behavior,” said the insider.

Another source said that Biel is likely looking to preserve her family amid the controversy and move on with their life.

“Obviously Justin drank too much this time, but Jessica believes he didn’t cheat on her,” the source said. “What’s most important to her in life is her family and being the best mom to Silas. She’ll never break up her family over something like this.”