It looks ok, but I think you should'nt avoid the Mime-Type header. Anyway, why don't you define the headers like in
code:
/* Para enviar correo HTML, puede definir la cabecera Content-type. */
$cabeceras = "MIME-Version: 1.0\r\n";
$cabeceras .= "Content-type: text/html; charset=iso-8859-1\r\n";
/* cabeceras adicionales */
$cabeceras .= "To: Maria <maria@example.com>, Kelly <kelly@example.com>\r\n";
$cabeceras .= "From: Recordatorio <cumpleanyos@example.com>\r\n";
$cabeceras .= "Cc: archivo@example.com\r\n";
$cabeceras .= "Bcc: chequeo@example.com\r\n";
Taken from the spanish PHP-doc