Спасибо всем, кто откликнулся. Все получилось! =)
Так выглядит код сервера:

PHP код:
<?
$to = $_POST["to"] ? $_POST["to"] : "mail@mail.net";
$from = $_POST["from"] ? $_POST["from"] : "mail@mail.com";
$message2 = $_POST["message"] ? $_POST["message"] : "some message";
$subject = "?????? ???????";
$fileatt = $_FILES['fileatt']['tmp_name'];
$fileatt_type = $_FILES['fileatt']['type'];
$fileatt_name = $_FILES['fileatt']['name'];
$file = fopen($fileatt,'rb');
$data = fread($file,filesize($fileatt));
fclose($file);
$headers = "From:$from";
$headers .= "\nReply-To:$from";
// Generate a boundary string
$semi_rand = md5(time());
$mime_boundary = "==Multipart_Boundary_x{$semi_rand}x";
// Add the headers for a file attachment
$headers .= "\nMIME-Version: 1.0\n" .
"Content-Type: multipart/mixed;\n" .
" boundary=\"{$mime_boundary}\"";
// Add a multipart boundary above the plain message
$message = "This is a multi-part message in MIME format.\n\n" .
"--{$mime_boundary}\n" .
"Content-Type: text/html; charset=\"utf-8\"\n" .
"Content-Transfer-Encoding: 7bit\n\n" .
$message2 . "\n\n";
// Base64 encode the file data
$data = chunk_split(base64_encode($data));
// Add file attachment to the message
$message .= "--{$mime_boundary}\n" .
"Content-Type: {$fileatt_type};\n" .
" name=\"{$fileatt_name}\"\n" .
"Content-Transfer-Encoding: base64\n\n" .
$data . "\n\n" .
"--{$mime_boundary}--\n";
mail($to,$subject,$message,$headers);
?>
И вот так, (большое спасибо
gloomyBrain), клиент:

Код AS3:
import net.request.field.File;
import net.request.field.MIMEType;
import net.request.Request;
import org.bytearray.smtp.encoding.JPEGEncoder;
import flash.net.URLRequestMethod;
import flash.net.URLLoader;
var myEncoder = new JPEGEncoder( 900 );
var myCapStream:ByteArray = myEncoder.encode (bitmapData);
var request:Request = new Request("http://server.net/mail.php", {
to:"mail@mail.ru",
from:"mail@mail.net",
message:"some message"
},URLRequestMethod.POST);
var file:File = new File("fileatt", myCapStream, "image" + new Date().getTime() + ".jpg", MIMEType.IMAGE_JPEG);
request.files.push(file);
var loader:URLLoader = new URLLoader();
loader.load(request.toURLRequest());
loader.addEventListener(Event.COMPLETE, report);