Yes, if you get onto the same scheme as him, and if that is Swiss, yours will be retroactively applied as well.

Apparently, all foreigners / B-permit holders have three months from the day they enter to arrange insurance. If you end up with a Swiss one, it will apply from the day you entered.

If you have your own foreign insurance, however, this is irrelevant (if you get permission from the kanton's health insurance office to use foreign insurance). But that is probably irrelevant for you since your husband is arranging the Swiss insurance already.

(It is not irrelevant for EU nationals who have insurance at home before they come to CH and maintain that insurance; they only need to show their European health insurance card with EU logo to the correct kanton's office within the said three months, then they do not require Swiss health insurance).

I would be careful though with the doctor, if they ask whether you are insured, you may have to explain as I get the feeling they do not like uninsured people as they may fear they won't get the money back; remember they often send you an invoice weeks later.