To fetch the body of a "sub part" do the following thing:
<?php
$partno = "2.1" // The first part of the second part
print_r(imap_fetchbody($mbox, $msgno, $partno));
// TODO: replace print_r for the proper function
?>
And remember... you can fetch the structure with
<?php
imap_fetchstructure($mbox, $msgno);
?>
then iterate the array of parts fetching the body.