As stated below, for the time being - you'll probably want to stay off the credit application due to A. your low credit score, and B. lack of verifiable income/length of time in your new job.
As for your husband, he could certainly apply solely for financing....but the question is are you going to want to purchase the type of property afforded solely using his income? I don't know the market in your location, so I'm not sure what you can "get" for what he could qualify for on his own. Keep in mind that in addition to the principal on the loan, unless you put 20% down, you'll most likely be paying mortgage insurance, in addition to interest, taxes, and homeowners insurance. Some exceptions to this would be if you found a Fannie Mae/Freddie Mac owned property that was eligible for HomePath/HomeSteps financing (only 3.5% down needs and no mortgage insurance required), or USDA financing (the property would have to "qualify" for this to be eligible). With any financing however, your debt to income ratios would still have to qualify - regardless of the loan product.
My suggestion would be to first figure out what you can COMFORTABLY afford on your own, using an online mortgage calculator, etc. Then, meet with a mortgage professional who can give you an idea of the amount of financing you would qualify for. Lastly, determine if that amount is going to afford you the type of property you want/need. If not, you may be better off waiting until you can qualify jointly. The last thing you want is to be "stuck" in a home you can barely afford, that doesn't even meet your needs.........simply because you want to buy NOW!
Hope that helps!