It's unfortunate the 3rd-party API returns the JSON in [["key","value"],...] arrays rather than {"key:"value", ...}. The latter would be much easier to parse into a typical class like this:
public class Foo
{
public string Received {get; set;}
[DataMember(Name = "Content-Type")]
public string ContentType {get; set;}
...
}
The way it returns is an anonymous list of values, containing more anonymous lists, where the 0 value is the key and the 1 value is the value.
I haven't tried it, but you may want to try deserializing to dynamic list of anonymous types, per this SO answer
List<JsonObject> jsonObject = JsonArrayObjects.Parse(json);
jsonObject.PrintDump(); // show data
Then for convenience, you could write a mapping routine to copy the jsonObject to a more readable class.
Update: i wrote a bit of code to test. Not that pretty, but it does work to access the parsed JSON as-is.
string json = @"[[""Received"", ""by luna.mailgun.net with SMTP mgrt 8765806286401; Fri, 14 Jun 2013 02:25:33 +0000""],
[""Content-Type"", [""multipart/mixed"", {""boundary"": ""199d7350597e43c0af0e4c814b8a35af""}]],
[""Mime-Version"", ""1.0""],
[""Subject"", ""Test Message""],
[""From"", ""Test Sender <sender@mydomain.com>""],
[""To"", ""Test Receiver <receiver1@mydomain.com>""],
[""Reply-To"", ""replyto@mydomain.com""],
[""Message-Id"", ""<20130614022533.18419.66130@mydomain.com>""],
[""X-Mailgun-Sid"", ""WyIzOTUwOCIsICJuZWlsLmRvYnNvbkBleGFsdGdyb3VwLmNvbS5hdSIsICI4ZjY3OCJd""],
[""Date"", ""Fri, 14 Jun 2013 02:25:33 +0000""],
[""Sender"", ""sender@mydomain.com""]]";
List<JsonObject> jsonObject = JsonArrayObjects.Parse(json);
// jsonObject.PrintDump(); // show data
string received = jsonObject[0].Values.First();
string contentType = jsonObject[1].Values.First();
List<JsonObject> contentTypeValues = JsonArrayObjects.Parse(jsonObject[1].Values.First());
string boundary = contentTypeValues[1].Values.First();
string mimeVersion = jsonObject[2].Values.First();
Console.WriteLine(string.Format("received: {0}", received));
Console.WriteLine(string.Format("contentType: {0}", contentType));
Console.WriteLine(string.Format("boundary: {0}", boundary));
Console.WriteLine(string.Format("mimeVersion: {0}", mimeVersion));