I was very lucky that my husband had been at his job for many years. He took all the sick days my first couple of years, though my dad helped out a little (so my husband could work a half day or go to a meeting).
Now that I've been there a few years, we split the time. If he takes a day, then I know I need to take the next one if at all possible and vice versa.
It stinks, but it really is part of parenting until they get older. It's not easy to take sick days when you are new, but you also need to be there for your kids. Either your boss will understand or he/she won't. You just have to trust that if your boss doesn't understand a parent needing to take time off for a sick child, this is not the right place for you to be. This is just one parenting issue that will come up, and it is definitely not a mom friendly place to be.
Just out of curiosity, is it possible your husband simply doesn't want to have to take sick time? If that's the case, you might want to talk to him about it and remind him how much easier your transition would be if he would take on that responsibility for awhile. I realize there are some jobs where it is really tough to take sick time, but he is a parent, too, and the two of you need to be a team on this one. He needs to take sick days, too.