You have enough deposit to get a loan but when you borrow above the 80% level you become liable for Lenders Mortgage Insurance (or some equivalent fee under another name). This is basically an insurance policy in favour of the Lender that will pay them the shortfall if you default on your mortgage. So if they have to sell the property and the proceeds are less than you owe the the insurance covers the difference. So you actually pay to protect the lender. Won't stop them coming after you but it is their backstop.
This is why we call this LMI fee a waste of your money. We encourage people to try and have 20% deposit but it is not always possible.
In reality you may need the 90%-100% mortgage so you just need to go to a mortgage broker and have him look for the best one to suit you. Ask for 3 different companies as often they will just use their favourite.
Once your husband can show 6 months in one company /job then it will be a lot easier to get a loan
Tips:
Don't forget you may qualify for the First Home Buyers Grant and the Stamp Duty Exemption. Having owned a home in the UK does not count so you may qualify !
Bring 2 years of your loan statements from the UK to show a good mortgage payment history and the same on any other loans you may have. Also if you have UK bank statements for your day to day account which show that you don't go overdrawn then bring these as well. While the banks may not ask for them a good Broker will mention them as part of the submission to a lender and this may get you over the line for a better rate or product.
Have a look at the
RateCity - The online comparison capital - Home site and get to understand some of the loans in the market and the type of rates you can expect. This is a great free information site covering all types of loans, credit cards etc. A Great place to start for a new arrival!
Hope this helps
Liam