Broadcast in March 2012, the two-part series was accused by one councillor of portraying the city in a bad light.
Channel 4 defended the show, saying it aimed to overcome preconceptions about people from different ethnicities.
The programme looked at how people from different backgrounds lived together in Bradford, West Yorkshire, and filmed them as they shared their lives.
Other British winners at Thursday’s event included Sky comedy Spy, which was named best sitcom, beating the BBC’s Twenty Twelve and The Thick of It.
In the arts category, The Great Pretender – a BBC documentary about Queen frontman Freddie Mercury – was favoured ahead of the Julien Temple documentary London: The Modern Babylon and a third nominee, Just Ballet from Austria.
More than 300 entries from more than 30 countries were submitted for the 2013 awards, which were held outside Switzerland for the first time in 52 years.