Any http request means two things: One, hackers might be snooping and reading both the request and the response. Two, hackers might be able to return a different website from the original one.
So if I access your website through http, and receive an https link back, hackers might learn about that https link, but all in all it's not less secure than an http link.
However, there is no guarantee at all that I received your website and not one provided by a hacker. So that https frame might not even be present on the correct site, only on the hacked one. And there's no guarantee at all where it points, therefore no security at all.
Once you start with http, as far as security is concerned, it's game over.