I'm sorry, but I just have to say, I would be more concerned about the XBOX than anything else. And it's not appropriate for your DH to say "Fine, you watch her." so he can play a video game. I can't imagine that ANYTHING on XBOX that your DH would want to play is appropriate for such a young child. He can delay his own gratification for that until she is in bed.
As far as the regular TV, signing, etc...I'd probably mix it up some too with educational shows...my kids loved pretty much everything on PBS, plus there are no awful toy commercials. My oldest also enjoyed those Baby Einstein videos...
And...as far as interaction, etc goes...well. My kids were probably HAPPY for me to turn on the tv and STOP talking to them, lol! I talk almost nonstop to babies, describing every moment of my day, what I'm doing all the time. Both girls were communicating before a year, with The Diva (now almost 5) speaking in complete sentances before her 2nd bday...
