They've migrated the BHN and TWC websites over to the Spectrum platform. In order to see TWC lineups, you have to go down to the bottom, where it opens up the legacy TWC website. Whenever you put in timewarnercable.com, you get re-routed to Spectrum.
Eventually, I would think all 3 companies will be on the same website. I'm not 100% sure on how to find the BHN pages at the moment. Charter's TV guide page, which I find to be the most accurate for legacy Charter systems, does not allow you to search anything for TWC/BHN systems yet.
There is some action it seems. I would guess Impact Network HD might have appeared on BHN systems. It's started to appear on both legacy Charter and legacy TWC systems. More legacy Charter areas are getting the missing HD channel package from TWC/BHN contracts. NBA TV HD is unevenly appearing for legacy Charter, so far only on areas with NBA teams. I've noticed it on systems in Massachusetts, North Carolina (specifically within the Charlotte market), Georgia (specifically within the Atlanta market), Wisconsin (within the Milwaukee market), Minnesota (within the Twin Cities market), and Southern California (within the LA market), whether or not some of these have received the other Spectrum channels. I don't know if this portends a good trend for the TWC/BHN areas that have the channel universally, if someday they'd keep it in Orlando and remove it in Tampa, for example. Everything else seems to be aligning, although legacy Charter is not adding the Spectrum SportsNets out-of-market, MGM HD or Fusion HD to TWC/BHN systems at this time. Some have reported issues with Sportsman Channel HD and MavTV HD in legacy TWC/BHN areas, so those could be endangered as options align, even though legacy Charter carries both universally (but threatened to drop Sportsman Channel last year).
The previously mentioned BabyFirst TV officially has an HD feed now that Verizon FiOS has added, it will be interesting to see if it finally appears for Spectrum. But everyone's grasping at straws for new channels. Especially BHN systems since they have everything and more than just about everyone else.