Of Batman's many non-suited allies, James Gordon is arguably one of the most important. As head of the GCPD, Batman finds not only a friendship in Jim, but a desire to work together with him for the betterment of the city. The two share a a powerful sense of justice, though Jim does think at times what Batman does goes too far. That said, he trusts Batman's judgement, and rarely feels that Batman has betrayed him.
In fact, after Batman is presumed dead in the New 52, it's Jim Gordon who is choosen to take over the mantle. He gave it up later when Bruce returned, but he did he best with the title.
Jim's connection with Batman has caused him a lot of pain, both knowningly and not. However, to protect Gotham City, Jim Gordon knows he must do what needs to be done in the name of justice.