I went through this for and it sucked hard core. There is a lot of pride, machismo, emotion going on inside him. Men are hardwired to support thier family. His acting lackadasical could be his cover for actually being scared to death. Maybe he's trying to act like it's ok for your sake.
My suggestions - what worked for me
1) Make being home really suck. cut off the cable, pawn the video game systems, and leave the kids with him a couple days a week. Start cooking a pot of Beans for dinner 5 nights a week. Make meatless dinners. It won't take long for him to want out of there!
2) be supportive, not nagging. Leave him nice notes to boost his confidence. Tell him regularly that he's still your hero and how proud you are that he is taking the transition so well. Build him up, don't tear him down.
3) apply very gentle pressure and hold him accountable. Check in as though you are checking the schedule - So, honey, what days do you plan to be out job hunting this week? I need you to pick up the kids, so let's take a look at your job hunting schedule for the week. Then ask at the end of the day where all he tried and how it went and give suggestions and compliments - wow honey, that was a great idea to go there, I wonder if they have another location you could try, or how about trying this that and the other tomorrow. That way it feels more like you are working as a team.
4) offer to help and then wait for him to take you up on it. Women think they are helping by asking questions. That is not helping, that is nagging. Help by offering to do things for him - honey, I would be happy to tweek your resume for you. I wouldn't mind submitting a few resumes for you, just let me know how I can help.
5) do it yourself! I helped mine get signed up with career builder, monster, etc. and helped him create a resume. Then, during slow times at work, I would go into all sorts of business websites and submit his resume directly. He put in so many, he couldn't keep track if it was one I did that called. I signed himup with a few temp services so he could still bring in money while job hunting. I networked at my job for him. For instance, I asked the UPS guy if they were hiring.
It worked - the guy has two full time jobs right now!