To retrieve inforamtion about message structure, use the ImapListFields.MessageStructure parameter in the GetMessageInfo or GetMessageList methods.

Following example prints requested information:

C#

// connect and login
Imap imap = new Imap();
imap.Connect(...);
imap.Login(...);

imap.SelectFolder("INBOX");

// retrieve information of emails envelope and structure
ImapMessageCollection col = 
    imap.GetMessageList(ImapListFields.Envelope | ImapListFields.MessageStructure);

// print the information
foreach (ImapMessageInfo item in col)
{
    Console.WriteLine("{0}: {1}", item.SequenceNumber, item.Subject);
    foreach (ImapMessagePart part in item.GetParts())
    {
        if (part.Kind == ImapMessagePartKind.Attachment)
        {
            Console.WriteLine("  {0} [{1} B]", part.FileName, part.Length);
        }
    }
}

VB.NET

''# connect and login
Dim imap = New Imap()
imap.Connect(...)
imap.Login(...)

imap.SelectFolder("INBOX")

''# retrieve information of emails envelope and structure
Dim col = imap.GetMessageList(ImapListFields.Envelope Or ImapListFields.MessageStructure)

''# print the information
For Each item As ImapMessageInfo In col
    Console.WriteLine("{0}: {1}", item.SequenceNumber, item.Subject)
    For Each part In item.GetParts()
        If part.Kind = ImapMessagePartKind.Attachment Then
            Console.WriteLine("  {0} [{1} B]", part.FileName, part.Length)
        End If
    Next part
Next item

Please note the ImapListFields flags are combined together with the OR binary operator (not AND) as shown in the imap.GetMessageList method call.