Iframes seems to work.
Refer to this article / video.
Text of the article to explain:
Instead of pasting the code from the embed code page of the registration form onto your website, paste it into a text document (using NotePad (PC) or TextEdit (Mac)) and name it "signup-form.html" or something like that. You can wrap the form in a div for styling and add some inline styles. Therefore, the HTML document will look something like this:
<style type="text/css">
</style>
<div id="sign-up">
at least 50 lines of code copied from MailChimp goes here
</div>
HTML- ( "signup-form.html" , ) - .
, ( , ), HTML iframe :
<iframe src="http://your-site.com/mailchimp-form.html" frameborder="0" width="654" height="200">
<a href="http://link-to-form-on-mailchimp-site" target="_blank">Anchor text saying "click here to sign up" or something like that for people whose browsers can't read iframes</a>
</iframe>