You'll need to confirm that a 403b is treated similarly to IRAs/401Ks when inherited. I can only speak from my experience/research when inheriting an IRA from my father... so the following is based on that, YMMV. Consult the plan's representative ASAP to make sure you follow all the steps needed properly.
Make sure if any distributions were needed to be taken by your parent, that they do so ASAP. Then make sure your second step is to set up the new account properly as an inherited account
In the case of an inherited IRA/401K, you have two options:
1. Take out all within a 5 year period. This is a poor option, as distributions are generally considered taxable income, so if the account has a large amount, you will find yourself pushed into a much higher tax bracket potentially. Try to avoid this if possible.
2. Set it up as a inherited (stretch) IRA. This means you can take required minimum distributions (RMDs or MRDs) for the rest of your life. By setting up the account as a beneficiary/inherited IRA/401K, you are the allowed to have the company set up the distribution on a yearly basis and they assess your age and the amount in the account each year and then you take X amount of money out to satisfy the RMD, but allowing the rest of the account to continue to stay invested. Some smaller (less savvy) companies force you to figure the RMDs out yourself, but you can roll the account to someplace like Vanguard or Fido and they'll do automatic calculations for your RMD, withholding taxes and transferring the remainder according to what you tell them. This is usually the best option, since your RMD is figured based off your age and you minimize the tax hit, and the account is tax deferred while at the same time it is still growing and you can invest the funds in anything you'd like. And in the case of 401k/IRAs (and likely 403b), you can take RMDs or more out with zero penalties - just pay taxes if they are owed.
If you fail to make this account (IRA/401K anyway) reclassified as an inherited version and take the distribution if needed for the parent before the deadline, you may automatically be forced to do the 5 year distribution, which could be potentially horrible for your taxes over that time period, so do get this dialed in with the representative as soon as you can.
The big issue I'd see with your plan is that you and your husband will still be working and have income from those jobs, and taking additional money out of the inherited 403b to fund your expenses means you'll be having to count all that in addition to your regular income on your taxes... meaning you may potentially have a HUGE tax bill (possibly with penalties assessed if you owe more than 1K, since the IRS thinks you should have been pre-paying if you go over that amount owed). And also keep in mind that if you have a taxable account and are currently enjoying paying zero on the cap gains/dividends because you're under the 15% taxable bracket, you'll also owe on those as well if popped over the 15% bracket due to the increased taxable income counted.
Again, consult the plan's representative to confirm how this should be handled as soon as possible. You should (again, based off my IRA stuff) have til the end of the year to get this set up and the distributions figured and the account reclassified, but the sooner you get this stuff figured out the less it will be hanging over your head and the more time you have to figure out how to make this money work best for your plans.
Finally, I am so very sorry for your loss. It may have been sudden or expected, but losing a family member is never easy.
