Thank you for using our forum. My name is ***** ***** I hope to assist you today.
I am very sorry to learn of your loss, please accept my condolences for your husband's passing.
You are not liable for your husband's hospital bills (your personal/separate assets are not subject to collections).
The same is true for your children (they are not liable for their father's healthcare expenses).
The only exception to this is if anyone has signed what is called a "guarantee" or "guarantor" contract with the medical providers where you agree to pay the medical bills if the patient, the patient's insurance, or the patient's estate are unable to pay for them.
In most cases such as your husband's what happens is that the healthcare insurance (medicare) will pay for his bills. They will get a lien against his interest in your family residence. However, they will not enforce this lien until you move out of the home (they will not foreclose on the property while you are living there).
If your husband's estate is probated, the healthcare providers will submit claims against the estate - so your husband's assets (bank accounts, etc.) will be subject to liquidation (reduced to cash value) and those assets can be used to pay his debts, including his medical bills - but if there are not enough assets to pay all of his debts, the creditors are left with balances that they cannot collect or enforce (again you are not liable or responsible for his debts).
If you find that you are being pressured or pushed by these creditors, hire an attorney to review the contracts and draft a letter on your behalf - this is usually far cheaper (and less stressful) than trying to fight these people off one letter after another - most creditors will act appropriately, but some do not, in which case hiring a local general practice attorney to help you out is worthwhile.