Using AJAX with Forms

Your add_action() calls for the AJAX handlers are too late.

Add these hooks earlier, the best action is probably wp_loaded:

add_action( 'wp_loaded', 'register_ajax_handlers' );

function register_ajax_handlers()
{
    add_action( 'wp_ajax_jp_ajax_request', 'jp_ajax_process');
    add_action( 'wp_ajax_nopriv_jp_ajax_request', 'jp_ajax_process');
}

See also: Debug AJAX.

This code should be placed in a plugin or in your theme’s functions.php.