When Googbot visits the site with the frame, all it will see is a frameset in the source code usually implemented something like this:
<frameset rows="100%,*" border="0">
<frame src="http://othersite.example.com/" noresize frameborder="0">
This will point Googlebot the place where you content is actually hosted. Googlebot will index the site there and never refer users to the site with the frame.
Neither are frame redirects good for users. As users navigate deep into your site, the URL that the user sees in the browser doesn't change. This make it hard for users to bookmark the part of the site they are interested in, or to share it with friends by copying the URL.
What you really want is for your blog host to fully host the blog under the correct domain name. This is usually referred to as a "custom domain". Most blogging platforms and web hosts support it, but how it is set up, and how much it costs differ widely from one host to another.