Funcunit testing process that switches from http to https.

I am trying to write a script that exercises the checkout process on one of my employers websites.  I have noticed that when navigation to the secure side of the process occurs where a user would enter their credit card number that the script stops running because of security errors in Chrome having to do with script running from a standard http session while the application has now moved to https.  This is not entirely surprising, but is there a way around this?  Is Selenium a better option for this type of use case and instead reserve pure funcunit for more focused testing of javascript widgets?

Thank you.