As your money situation isn't too terrible by the sound of it, here's some practical advice.
First thing is not to panic.
Second thing is for DH to find out what any references from his ex-employer will say. Hopefully it'll only confirm his job title, start date and end date. He may still be able to ask them to agree references even after he's left if they're willing to be a bit nice about it. It's worth asking.
He can then either leave his last job off his CV, or explain it away as a short-term contract at his interviews.
Next, he needs to get his CV up to scratch. Focus on achievements over responsibilities. Provide data, for example; "I restructured the team, resulting in an increase in customer Satisfaction of 30%" instead of "I was responsible for managing the team and ensuring customers were satisfied by our service".
Keep him applying "upwards". If he has 50% of the skills and experience needed, that's good enough to justify applying for roles.
Get him to do online training to improve his skills/knowledge. Even if he doesn't pay for any certificates, the improved knowledge should help in interviews.
Male job hunting a full time job 9-5, Monday to Friday. Have him apply online and also follow up by calling the recruiter. He will then get himself at the forefront of recruitment agents minds. They may then actively start pushing him to their clients.
Get him on LinkedIn, both posting content and commenting on others, daily. Also have him connect to others in his industry, both at his level and above. Also hunt down recruiters in his industry and connect with them - they often post roles on there before they hit the job sites.
Indeed, cv-library, reed and then any industry-specific job sites. Check them every couple of hours, sorted by latest jobs first. If he can get in early, a recruiter is more likely to see his application before it gets lost in a sea of applicants.
What industry is he in by the way?