Thanks @webdev for pointing me to the solution:
Script in the head:
<script>
$(document).ready(function() {
var windowURL = window.location.href;
console.log(windowURL);
if (windowURL.indexOf('noheaderfooter') > -1) {
$('#header').css('display', 'none');
$('#footer').css('display', 'none');
}
});
</script>
Content of the page within the iframe looks sth like this:
<div id="header">
…header content…
</div>
<div id="footer">
…footer content…
</div>
And then I load the content into the iframe sth like this:
<iframe src="…domain.com/page?noheaderfooter">