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It looks to me like the code you need to modify is in at least 2 places - modresume.php, line 79 & ./admin/modresume.php line 62.
le="color: #000000"><?php $allowed_mimetypes = array('application/msword', 'application/pdf');
You should be able to just add the mimetypes you need there. Although you might want to visit the author's website and ask him where else this might need to be changed.
I don't use this module, and don't have it installed, so make sure you backup your site first before trying this...
