The NBC series follows a gay couple in Los Angeles (Justin Bartha and Andrew Rannells) who meet a single Midwestern mum (Georgina King) who becomes their surrogate.
NBC's decision to post the pilot online, which already aired during the Olympics, comes after its Utah affiliate KSL-TV pulled the show from its fall lineup because of its gay content.
The New Normal was deemed "inappropriate" for the KSL-TV brand, "especially during family viewing time".
The Gay & Lesbian Alliance Against Defamation (GLAAD) condemned KSL-TV for being "deeply out of touch with the rest of the country".
"Same-sex families are a beloved part of American television thanks to shows like Modern Family, Glee and Grey's Anatomy," GLAAD President Herndon Graddick said in a statement.
The New Normal will air on Tuesday, September 11 at 8.30pm on NBC.