To be honest, it doesn't sound as though you want to go out with your husband to this party. You have options - you could both stay home, he could go alone, or you could continue search for alternative babysitter so you both could go. Is this a special party? Best mate's landmark birthday? Or just a general pissup? Is this something that really, really matters to him?
If not, do you go out regularly as a couple? Can you say, well, we can't do this party, but to compensate we'll be going out together next Thursday?
My DH works away in the week, but very occasionally (usually about twice a year) I will ask him to come to something with me on a week night. He knows I only ask if it is very important to me and that I really, really want him there, so he moves heaven and earth, and rearranges his schedule to make it. I really appreciate this.
How much notice do you have to make alternative arrangements for this party, if you do want to go?