So actually NEITHER of you are working?
Why can't you work and he stay home with your child?
"He couldn't cope as a stay at home dad" tough! That or he gets a job!
Why did you move when you were pregnant, leaving a job as a result?
Also you could both find out about GETTING more qualifications, make applications - you should be doing that now if you intend to study 2018/19 academic year, usually cut off is around Easter.
All that said he DOES maybe need to get a grip and realise very few employers will want HIM with no quals. In fact are you sure it's not him being rejected but saying he didn't want to do "X" job to save face?
If he's no qualifications at all that could also explain why the army idea vanished. People mistakenly think they'll "take anyone" not true. Qualifications are needed for some roles, plus has he any convictions? Medical issues?
Or do you think he's going into interviews with an attitude?
What does he do at home? Feed, clean, change baby? Cook and clean house?