You'll need to access your templates fix this issue. Log in to your control panel, and visit:
Design -> Templates -> Template Manager
Most likely, you'll have a template group named "Embeds", "Includes", "Global", "Layouts", or something along those lines. In that template group you will likely have a template named "head" or "header". What we are looking for here is the template that outputs your website's
<head> tag, which is where your stylesheets'
<link> tags are going to be. I would edit those tags so they point at a protocol-relative URL instead of a hard coded one. So one example for you would be to convert this tag:
<link href="http://www.mysite.com/assets/css/style.3.0.2.css" rel="stylesheet" type="text/css">
<link href="//www.mysite.com/assets/css/style.3.0.2.css" rel="stylesheet" type="text/css">
This is actually an anti-pattern at this point, but it is probably the best way for you to move forward for now. You'll want to enforce SSL on your site at all times, but that is beyond this answer's scope, and using a protocol-relative URL will work now and after you enforce SSL. After you do enforce SSL, you should change those links to start with
https, but they will still work with the protocol-relative URL so nothing should break.