I understand your concern, but the terms under which the policy is offered is to provide the cover for up to 12 months. The easiest way the insurer has chosen to get the policyholder to show this is through the JSA evidence. What the insurer clearly wants to avoid is continue forking out for someone who merely decides to bum around for 12 months just to be able to collect the money - not your situation, I entirely understand.
By all means check, but I am very confident you will find that the insurer just wants evidence that the policyholder is searching for work during the whole period of the claim. After the 6 months period, your husband will still be signing-on even if unable to be paid JSA. That should be enough.