Your husband has to join new company in a month's time .
He may represent to the reasonable superiors above him, and in HR, and take them into confidence that he is sincerly willing to conclude the work with him, and if they have selected a new guy even train and handover the charge to new guy,and give the reference of some good candidates and that he is willing to help the old colleagues and employer.
And that he has firmed up his next venture for better prospects, and he has to join with in a month.
If required he may escalate to higher ups.
The old company can relieve him and wave off the notice pay also, and can give good comments in work experience certificate, and a good reference check.
He may manage with the new employer, and point out that he is in discussion with the old employer for a smooth transition and shall send the resignation letter.
He has the option of sending the resignation letter, the old company may ask to remit the notie pay,or deduct the notice pay from his full and final settlement. He can ask for work experience certificate/relieving letter/No dues Certificate/Form 16....