M.B.
There was a similiar question on here not too long ago that a dad posted and there was quite a bit of backlash at the dad for not recognizing that he shouldn't be posting it to a forum to make a point... not sure if you'll get the same reaction but I thought about that when I read your post.
First off, my house has a similiar makeup with mostly wood floors and cement-like tile.
I don't think that if your daughter is moving about that you should be out of her sight. Things can happen in literally seconds (the dad's question was about the mom walking out of the room while the kid was eating), my friends 10 month old son had to be taken to the hospital because when she swept, she'd missed a single unused staple. He ate it and it got caught (literally into the fleshy part of his throat) and had to be surgically removed.
But back to my situation, my husband would let our daughter toddle out into the cement-like area of our house and every time she'd fall and hit her head. I got upset with him everytime. The way they move around and fall etc is natural but it doesn't hurt to be cautious.
The solution was putting up gates to the areas where she was most likely to get hurt (the cement areas) and putting down rugs on the wood floors. If she's falling over from a sitting position, try a bumbo seat that will help her stay upright or put pillows around her.
Your husband is worried about your daughter. That's not a bad thing but you two need to talk to each other (TALK being the operative word here) about what you expect of each other. You're the easy going "kids will be kids and they get hurt" (that was my husband) Your husband is the overly cautious one (that's me) there is a middle ground and the two of you need to work together to find solutions, not prove who is right and who is wrong.
As your daughter gets older, he'll relax a little more about the things she's doing and as she does get hurt a little more, you'll become more cautious. Caution isn't that bad though. There are too many stories of a mother who went to the bathroom and left the lid of the washer up and the kid climbed on a chair and fell in and drowned (2-5 minutes in the bathroom) kids who choke on seemingly safe foods (it only takes 4 minutes for brain damage to occur), eating or inhaling something accidentally left where someone can't see them.
The best defense is a perfectly sterile environment or supervision appropriate to the age.
So... my final thought? Your husband is not entirely wrong in worrying but he's wrong in going off on you about it. You need to be a team.