Conditional check for front-end which includes ajax

DOING_AJAX and WP_ADMIN (this constant is checked within is_admin() ) are defined in admin-ajax.php and set tro true. Both are not very helpfull in this situation.

Add a parameter to your ajax request if the request come from the front-end:

<?php

function my_action_javascript() {

?>
<script type="text/javascript" >
jQuery(document).ready(function($) {

    var data = {
        action: 'my_action',
        frontend_request: true,
        whatever: 1234
    };

    // since 2.8 ajaxurl is always defined in the admin header and points to admin-ajax.php
    $.post(ajaxurl, data, function(response) {
        alert('Got this from the server: ' + response);
    });
});
</script>
<?php
}

In your ajax callback you can now check if the parameter is present and set to true:

$from_frontend = isset( $_REQUEST['frontend_request'] ) && ( TRUE === (bool) $_REQUEST['frontend_request'] );
$doing_ajax = defined( 'DOING_AJAX' ) && TRUE === DOING_AJAX;
$is_frontend_request = $frontend && $doing_ajax; 

if( TRUE === $is_frontend_request ){
    // yes, this request came from the front-end
    echo 'On frontend';
} else {
    // no, we are somewhere else
    echo 'Somewhere else';
}