The following code doesn't use MAPI as such, but it does open the "Compose Mail" window with arbitrary attachments.
(actually, it's entirely untested but I dug it up in an application that I believe to have worked)
using Microsoft.Office;
using Microsoft.Office.Core;
...
Outlook.Application outlook = new Outlook.Application();
Outlook.MailItem mail = (Outlook.MailItem) outlook.CreateItem(Outlook.OlItemType.olMailItem);
mail.BodyFormat = Outlook.OlBodyFormat.olFormatRichText;
mail.HTMLBody = "stuff";
mail.Subject = "more stuff";
string file = File.ReadAllBytes(...);
mail.Attachments.Add(file, Outlook.OlAttachmentType.olByValue, 1, file)
mail.Display(false);