This is one of the biggest misunderstandings going on currently in the proxy market.
First of all, most proxy services advertise their proxies as HTTP/S or HTTPS.
In reality they are HTTP proxies (notice: without the S) because these proxies do not have their own SSL certificate (for the S to append to the HTTP).
However, this doesn't mean that these proxies are not secure. Actually, they are because HTTP proxies allow the transport of a website's SSL certificate. That's why, when you visit a website via a HTTP proxy, you will see the little green lock in the address bar (because the proxy server transported the SSL certificate of the website's web server).
This is what most services offer - a secure HTTP proxy that can transport websites' SSL certificate to make your connection secure.
On the other hand, true HTTPS proxies have their own SSL certificate. And using them (real HTTPS proxy) will raise a certificate warning in your browser because the SSL certificate served through the proxy server will be the proxy server's one and not the website's one. So Chrome of Firefox will see this as a conflict.
So, bottom line, HTTP proxies are what you need to connect to websites without any issues. And as soon as you connect to a website, the SSL handshake with the website's SSL cert will take place and your connection will be HTTP/S.