Add certificate to HTTPS call with BouncyCastle and C#

Question

I need to make a HTTPS request and add a certificate to this request to make a double certificate check (client and server) in C#.

Here is the code I'm using for now. I didn't find documentation on how add a certificate to my request ?

using (var client = new TcpClient("serverName", 443))
{
    var sr = new SecureRandom();
    var cl = new MyTlsClient();
    var protocol = new TlsClientProtocol(client.GetStream(), sr);
    protocol.Connect(new MyTlsClient());

    using (var stream = protocol.Stream)
    {
         var hdr = new StringBuilder();
         hdr.AppendLine("GET /Url/WebService.asmx?wsdl HTTP/1.1");
         hdr.AppendLine("Host: serverName");
         hdr.AppendLine("Content-Type: text/xml; charset=utf-8");
         hdr.AppendLine("Connection: close");
         hdr.AppendLine();

         var dataToSend = Encoding.ASCII.GetBytes(hdr.ToString());

         stream.Write(dataToSend, 0, dataToSend.Length);

         int totalRead = 0;
         string response = "";
         byte[] buff = new byte[1000];
         do
         {
              totalRead = stream.Read(buff, 0, buff.Length);
              response += Encoding.ASCII.GetString(buff, 0, totalRead);
         } while (totalRead == buff.Length);
     }
 }