From your post, you husband might be very frustrated with putting conversations on hold-- likely, some are necessary conversations-- because the baby is present.
Everyone is different-- I don't think your opinions are wrong, and I think I get where you are coming from. I myself was extremely wary about arguing with my husband in front of my son, and this was also hard on our relationship.
A mentor suggested something to me around that time which has stuck with me: it's not just about the disagreement, it's about the resolution too. My husband and I sometimes get upset with each other, and our son sees this. He also sees us talk about our feelings in a genuine way, come up with ideas, teamwork solutions together and that those moments pass. We don't stay mad forever, and nothing is irreparably broken. He sees that his mom and dad have strong emotions, just like some he experiences too. He sees people move from conflict (which can potentially threaten a relationship) into resolution, and sees the relationship still intact.
When we sometimes get upset with our spouses, we are normalizing a range of emotions for our kids. Let's face it, we all get upset from time to time, we all experience anger, hurt, and frustration. If we never saw our parents get reasonably upset, we might have felt there was something bad about ourselves for experiencing those feelings. And so when our kids do get upset, if we've given them context for it, they know it's normal to have strong feelings from time to time, and that they can be worked through and resolved.
This is not a blanket statement, by the way. There are healthy and respectful ways of being angry and working through problems. Absolutely, we should be modeling "how" to move through conflict, and this means avoiding pettiness, namecalling, global language ("you always.... you never..."), throwing the kitchen sink at each other (unloading at them with the laundry list of all past wrongs), and of course, using physical violence.
However, when we use "I" statements to convey our frustration, when we state clearly what we are wanting, and try to keep things solution oriented, we do well to have some arguments in front of our kids.
How would they learn to problem-solve with their friends if they didn't see it from us?
If you and your husband can "fight fair", see if you could try getting a little more comfortable with it. If not, look into counseling, because then it's likely that this isn't the only thing you two don't agree on. Otherwise, this could help your husband feel a little more human around your daughter. Remember, she needs a human dad, not a perfect, never-arguing one. Or what's going to happen when she's old enough for him to argue with her?! It happens!:)
H.