In my view there are only a couple of contributors on Answerbank with enough knowledge to answer these type of questions adequately.
The first point is that if DH has been paid wages in lieu of notice as part of his overall redundancy payment, he will not be able to be paid Contribution-based JSA until the expiry of that notice period. At the end of the notice period, he will be able to claim it whilst seeking work, for 6 months or until he finds another job.
The second point is that he should register at the JC in any event (and should have done so already) because, even if he is barred from getting CB-JSA as para 1 above, he will get credits for NI from the date he registers, and not from the point he is entitled to any JSA money. It is sometimes unclear if one needs the credits to achieve a 'qualifying year', but my advice is to register at JC anyway, firstly to be sure based on current rules, secondly because successive Government persist in changing the rules over the last 20 years so who knows what additional hurdles may be put in place between now and when he retires.
Thirdly, to get a qualifying year, one has to contribute NI on at least 52x the Lower Earnings Limit (LEL) in a tax year. In 2015/16 this LEL is £112 per week, so the threshold is earnings of £5824 in the tax year. Now if he's the main bread-winner he will have gone well over this figure already this tax year (and so will have already 'qualified' to have this year count as one of the 30 he needs), HOWEVER if he was in the company pension scheme and 'contracted-out', this crazy business whereby one's new State Basic Pension gets reduced because of being contracted out may come into play.
Hence to be of getting maximum State benefit from this unfortunate situation, get him to register at the JC.