Any included file (incl. your CSS) must be https. Otherwise browsers will give warnings or refuse inclusion. For images, you can use Ogone's little images hosting that is included with their service.

The way to avoid that is to put CSS into head of HTML directly within <style> . That way you avoid putting extra files.

Btw, SSL certs do not have to be expensive: 2 examples (3 or 5 years cert for our first offering! and even free 1-year certs or inexpensive 2-year ones on second link):

hosting.joomlapolis.com/portal/cart.php?gid=10

www.startssl.com/

But private IP that is required and hoster work to activate IP+SSL can be.