A source confirmed their relationship to PEOPLE on July 29 amid the the stars' press tour for 'The Naked Gun' — but their flirty premiere tour had tipped people off that they might have had a romance brewing.

On Monday night, the costars attended the New York City premiere of their upcoming film with their respective kids. Anderson walked the carpet with sons Dylan Jagger Lee and Brandon Thomas Lee, while Neeson was joined by his sons, Micheál Richardson and Daniel Neeson.

The film stars Neeson as Frank Drebin Jr., son of Leslie Nielsen’s Detective Sergeant Frank Drebin, as he follows in his bumbling father’s footsteps and must solve a murder case to prevent the police department from shutting down.