I would suggest you to try the following code:
    $notification = array("applicationId" =>"32768",
            "schemaId"=>"32771",
            "topicId"=>"32768",
            "type"=>"USER"
    );
    $ch = curl_init();
    $headers = array();
    $headers[] = 'Content-Type: multipart/form-data';
    curl_setopt($ch, CURLOPT_USERPWD, "devuser:devuser123");
    curl_setopt($ch, CURLOPT_URL, 'http://localhost:8080/kaaAdmin/rest/api/sendNotification');
    curl_setopt($ch, CURLOPT_RETURNTRANSFER, 1);
    curl_setopt($ch, CURLOPT_TIMEOUT, '3');
    curl_setopt($ch, CURLOPT_HTTPHEADER, $headers);
    curl_setopt($ch, CURLOPT_POST, 1);
    curl_setopt($ch, CURLOPT_POSTFIELDS, array(
                                            'notification' => json_encode($notification),
                                            'file' => '@' . 'notification.json'
                                         ));
    $content = curl_exec($ch);
    print $content;
    curl_close($ch);
Basically this code the same thing as bash command you provided, but with one difference - it does not provide Content-Type for notification param.
Instead of 
--------------------------5766b31cc6648aa7
Content-Disposition: form-data; name="notification"
Content-Type: application/json
{"applicationId":"32768","schemaId":"32771","topicId":"32768","type":"USER"}
--------------------------5766b31cc6648aa7
it sends 
--------------------------dd3a987c4561b96a
Content-Disposition: form-data; name="notification"
{"applicationId":"32768","schemaId":"32771","topicId":"32768","type":"USER"}
--------------------------dd3a987c4561b96a
However, I think this still should work fine. If not, please get back to me and I will provide you a different script that won't be that nice and clear, but will work.
================ UPDATE 1 ====================
Here's ugly script that must work
function multipart_build_query($fields, $boundary){
  $retval = '';
  foreach($fields as $name => $v){
        $data = $v[0];
        $filename = (isset($v[1])) ? '; filename="' . $v[1] . '"' : '';
        $type = (isset($v[2])) ? 'Content-Type: ' . $v[2] . "\n" : '';
        $retval .=  "--$boundary\n" .
                "Content-Disposition: form-data; name=\"$name\"$filename\n$type\n" .
                "$data\n";
  }
  $retval .= "--$boundary--\n";
  return $retval;
}
    $notification = array("applicationId" =>"32768",
        "schemaId"=>"32771",
        "topicId"=>"32768",
        "type"=>"USER");
    $post_data = array(
        'notification' =>       array(
                                        json_encode($notification),
                                        null,
                                        'application/json'
                                ),
        'file' =>               array(
                                        file_get_contents('notification.json'),
                                        'notification.json',
                                        'application/octet-stream'
                                )
    );
    $boundary = md5(time() . mt_rand(1, 65536));
    $ch = curl_init();
    $headers = array();
    $headers[] = 'Content-Type: multipart/form-data; boundary=' . $boundary;
    curl_setopt($ch, CURLOPT_USERPWD, "devuser:devuser123");
    curl_setopt($ch, CURLOPT_URL, 'http://localhost:8080/kaaAdmin/rest/api/sendNotification');
    curl_setopt($ch, CURLOPT_RETURNTRANSFER, 1);
    curl_setopt($ch, CURLOPT_TIMEOUT, '3');
    curl_setopt($ch, CURLOPT_HTTPHEADER, $headers);
    curl_setopt($ch, CURLOPT_POST, 1);
    curl_setopt($ch, CURLOPT_POSTFIELDS, multipart_build_query($post_data, $boundary));
    $content = curl_exec($ch);
    print $content;
    curl_close($ch);
----- UPDATE 2: Raw request added -----
POST /kaaAdmin/rest/api/sendNotification HTTP/1.1
Host: localhost:8088
Authorization: Basic ZGV2dXNlcjpkZXZ1c2VyMTIz
User-Agent: curl/7.43.0
Accept: */*
Content-Length: 430
Expect: 100-continue
Content-Type: multipart/form-data; boundary=------------------------f03cb5aef819a622
--------------------------f03cb5aef819a622
Content-Disposition: form-data; name="notification"
Content-Type: application/json
{"applicationId":"32768","schemaId":"32771","topicId":"32768","type":"USER"}
--------------------------f03cb5aef819a622
Content-Disposition: form-data; name="file"; filename="notification.json"
Content-Type: application/octet-stream
asdasdasdad
--------------------------f03cb5aef819a622--