They seem to honestly need help right now. I think trying to befriend her and see what she really needs to be able to find work might be a better task to take on.
In Habitat we always reminded everyone at the monthly board meetings that the program was to be a hand up not a hand out. Teaching these families to be good stewards of their resources was a huge undertaking. I was NOT on the nurture committee! I am just not that patient.
The guy needs to find work. He's probably been turned down so many times he has given up. He needs to find work. It might help to know what field he's looking in. For example, if he's a mechanic and can't find a job he could start taking jobs at home if he has tools. If he's a chef and has to be bonded then of course he needs to be retrained for another career. So he might need to fill out financial aid papers and go to school. His financial aid could help to pay the bills while he is learning to do something he'll enjoy and find fulfilling.
She might need to understand that having a baby isn't the end of the world and she needs to get a job. She can go to work 6 weeks after giving birth. She can get free child care if their income is so low. If he's filling out applications and looking or going to school and she is working then their income will still be low, then their co-pay would be really low if anything at all.
They can get WIC, food stamps, child care assistance, financial aid, all sorts of help. They just need a kind helping person to help them get on the right path.