In most circumstances the interest charged on your mortgage will be more than what you could accrue on your savings, so it would be advisable to clear as much of your mortgage as you can, as soon as you can.
However, your situation is difficult. The fact that you have limited security on your 'next month' income, means you are not in a position to use up all of your funds.
If I were you, I wouldn't be concentrating on paying off your debts, just now. I would make sure your savings are working as best they can for you. You can look at what offers are out there in the "Financial Best Buys" Thread of this website.
Whilst you are out of work, you must be strict on your spending habits and build a short term budget, which allows you to survive on most of your partners income and if need be, some of your savings. It is very important you meet every repayment on your mortgage and personal borrowings, as the last thing you want it to default on either and impair your credit rating for the next 5 years.
How have you been coping with regard to your monthly financial commitments? i.e bills, credit cards, loans, mortgage repayments, etc.
Jon