I believe you actually could breed Thamnophis with Nerodia. They're both very closely related live bearing snakes. And as someone mentioned that they can't because they're different genus...people breed Lampropeltis with Elaphe, Lampropeltis with Pituophis, etc. There was a wild Lampropeltis getula californiae X Pituophis catenifer catenifer found in California in 2005. I believe they are just as far apart as Thamnophis and Nerodia...

Now, I definitely don't condone the mixing of them, I just believe that is possible.