Hey folks, thanks to your suggestions, I have solved it.
In the template's index.php there were 2 calls made using http:// and in the helper file you indicated there are 26 calls. I replaced all of these using theur https:// equivalents, which solved it, and Chrome now is not complaining about the site anymore.
One interesting aspect: I have read somewhere that it could be possible to execute these calls with the resource called like this:
//resourcename.domain.com
instead of using http:// or https://
they claim that using //resource would then be converted into http or https, depending on the protocol being used, so not causing any errors, in any case.
I haven't tried this myself to be honest. I went straight to the https:// replacement, but I wanted to ring this bell in case you guys want to make some tests and then decide upon.
Again thanks for the help, issue solved !!
Regards AG