Are Yusuke and Jin half brothers?
I think I found the episode you were talking about: Episode 107: The Demon World Tournament Begins. The episode includes the battle between Jin and Soketsu, one of Raizen's old friends. According to the subtitles on Funimation's site, Soketsu never mentions Jin's father. There is a flashback to a fight between Raizen and Soketsu, however. Soketsu mentions that Jin is tenacious just like he was when he fought Raizen. Jin and Soketsu go on to say they both want to fight the son of Raizen (Yusuke).  This wiki page mentions that Soketsu erroneously calls Jin the son of Raizen in a variant of the English dub: http://yuyuhakusho.wikia.com/wiki/Souketsu.

So, Jin is not really the son of Raizen. This is just an error in translation. Even if he was, he wouldn't be Yusuke's brother (or half-brother). Yusuke and other characters call Raizen Yusuke's father, but he actually isn't. Raizen is Yusuke's ancestor, not his father.

Conclusion: Jin and Yusuke are not brothers