Your going about it in a way that was unintended. Your javascript code should probably look something like this:
$('.custom_media_upload').click(function(e) {
e.preventDefault();
var custom_uploader = wp.media({
title: 'Custom Title',
button: {
text: 'Custom Button Text'
},
multiple: false // Set this to true to allow multiple files to be selected
})
.on('select', function() {
var attachment = custom_uploader.state().get('selection').first().toJSON();
$('.custom_media_image').attr('src', attachment.url);
$('.custom_media_url').val(attachment.url);
$('.custom_media_id').val(attachment.id);
})
.open();
});