I wish there was such a thing as a "non-judgemental" way to tell him, one of his worst qualities is that he's extremely defensive. I do encourage him to take her on errands which he does but all the rest of the time she's plopped in front of the tv.
I guess I've never directly said she has to fight for attention... I just wish he could see what I see. Everytime I even so much as mention it he gets pissed off at me and it starts a fight.
I believe there can be a non-judgemental way to do it, though I know it can be really hard, especially when you're cheesed off.
Finding the right way starts in your own head, asking the question: "Why does he find it hard to enjoy our baby without distraction?" There could be a lot of answers to that question. Maybe he has a super-short attention span (too much TV as a kid?
) and finds more than 10 minutes of intensive concentration too much. Maybe he feels idiotic playing games or reading books with LO because it's 'unmanly' in front of the flatmate. Maybe he has ideas about parenting that are very firmly rooted in the idea that fathers are 'hands off' and mothers are 'hands on'. Maybe he is scared of ever admitting being wrong about something because he grew up being told that when he 'failed' he was less lovable. That's one that brings out defensiveness big-time for quite a few people. Maybe he absolutely genuinely doesn't see the harm in it - a lot of people subscribe to the "I grew up with TV and I'm fine" without really being able to objectively evaluate the effects it might have had on them.
Once you have it in your head that there are possible answers to that question that aren't just "He can't be bothered" or "He's too pig-headed to listen to sense", then you're ready to ask him in a non-judgemental way why he's struggling with spending TV-free time with your daughter. And you have to really listen to the answer and then try to solve the problem based on the ACTUAL answer he gives, and not on the idea "Well, he SHOULD feel this way/do it the way I want him to do it." Maybe that means you have to accept that he will never look after your daughter without the TV on. In that case, you have to decide whether it's more important to you that you get some break time, or that she doesn't get plopped in front of the TV, much as that is an unpleasant decision for you to have to make.
I find defensiveness is always a means of covering up fear. I suspect his fear is that he doesn't know how to be a hands-on father to a daughter so he defaults to using the TV as a babysitter. Ironically, it's the deflecting of responsibility that makes him the bad parent. Fears tend to work that way though - unless you can acknowledge them and deal with them, they turn you into the thing you don't want to be.