How to ajaxify wordpress theme

I want to Ajaxify my theme.
this is my index.php:

and this is my ajax.js file to ajaxify my theme:

In my website I’ve homepage and one custom post type. this is my custom post type:

now when I open homepage everything is ok. when I click on content that’s open my custom post type it opens that without problem. but when I go back to my home page I get a lots of errors in console. because ajax get header and footer again and if I go to another post and open my homepage again I will have more than one time <Doctype html> and header and footer section and it will be create lots of errors.
Please tell me what should I do to avoid loading header and footer more than one time.
Thanks