If you are not employed with the agency which established your 403b plan - you may access your funds as you wish.
If you are still working...
A retirement plan may, but is not required to, provide for hardship distributions. Many plans that provide for elective deferrals provide for hardship distributions - you need to contact with the plan administrator and verify your plan rules.
If your plan provides for hardship distributions, it must provide the specific criteria used to make the determination of hardship. Thus, for example, a plan may provide that a distribution can be made only for medical or funeral expenses, but not for the purchase of a principal residence or for payment of tuition and education expenses. In determining the existence of a need and of the amount necessary to meet the need, the plan must specify and apply nondiscriminatory and objective standards.
Please be aware that the hardship distribution is generally included into your income and in additional might be a subject of 10% penalty if you are below 59 1/2.
Let me know if you need any help.
If you wife is the owner of the retirement plan account - she would be the one who takes a distribution.
As you are living together - the hardship situation is determined based on your family finances - and the fact of your unemployment does matter.
However - please be advised that most - but not all employers provide a hardship distribution option.
Another option is that your wife will take a loan from her retirement account - and will pay it back with each paycheck.
The advantage of such option is that there will not be any tax liabilities because the loan is not treated as a distribution.
However - that would be the same situation - the law allows, but is not required plans to, provide loans - your wife needs to contact with the plan administrator and verify your plan rules.