The following assumes that your husband's employer had more than 20 employees.
At the time your husband left his job, you should have received information as to how to continue his insurance at his own expense. This is called COBRA and it is mandatory that the employer provide this information within either 14 or 44 days (depending on how their plan is administered) of the termination of the coverage. Electing COBRA is optional - it is entirely up to you whether you want to do it or not. But unless your husband was fired for gross misconduct (I'm not suggesting he was; just telling you what the law says) the employer was required to make the offer.
The ONLY way you can avoid responsibility for this bill is if you can show that the employer NEVER provided you with option. If they did, and you didn't read or respond to the material, then they have no liability. Their only responsibility is to provide the option. They are not required to follow up with you to determine whether or not you want it. You have 60 days from the date of the notice to make the decision and 45 days from the day you sign the election form to send in the payment. If you fail to do so, the employer has no more responsibility in this matter.
If they did not ever submit the information to you, then they MAY have liability for the bill. You'll have to run that one by the Department of Labor. However, if they did submit the paperwork to your last known address, then they are completely off the hook. They are also off the hook if they can show that they sent it, even if you never received it. For example, if they sent the information to the last address they had on file, but you had moved and not told them (this happens more often than you might think) they are not liable. Essentially they are only responsible for sending the info, not for acertaining that you received it.
I have to tell you that most employers are pretty savvy about COBRA and it's pretty unlikely that they never sent the info out. I can't say it's absolutely impossible, but I have a feeling you're going to be stuck with the bill regardless.
Why in heaven's name did you think the insurance would continue after your husband's employment ended? And did you ever ask whether or how long it would continue, or did you just assume their insurance would pay for the surgery of someone who was no longer employed by them?
If the employer had less than 20 employees, then COBRA does not apply as the employer is not required to offer it in that situation. Should that be the case here, then it's up to state law whether they are required to offer a continuation to terminated (or resigning) employees. Some states do require that. Most don't.