A first attempt at configuring the SOAP request programmatically

firstDraftClient.cs

AsymmetricSecurityBindingElement sec;

sec = (AsymmetricSecurityBindingElement) SecurityBindingElement.CreateMutualCertificateBindingElement(
    MessageSecurityVersion.WSSecurity10WSTrust13WSSecureConversation13WSSecurityPolicy12BasicSecurityProfile10); 
sec.DefaultAlgorithmSuite = SecurityAlgorithmSuite.TripleDesRsa15;
sec.IncludeTimestamp = false;
sec.AllowSerializedSigningTokenOnReply = true;
sec.MessageProtectionOrder = MessageProtectionOrder.SignBeforeEncrypt;
sec.EndpointSupportingTokenParameters.Signed.Add( new UserNameSecurityTokenParameters( ));

CustomBinding binding = new CustomBinding();

binding.Elements.Add(sec);
binding.Elements.Add(new TextMessageEncodingBindingElement(MessageVersion.Soap11, Encoding.UTF8));
binding.Elements.Add(new HttpsTransportBindingElement());

EndpointIdentity ei = new DnsEndpointIdentity( "DPMedsHistory");
EndpointAddress ea = new EndpointAddress( new Uri("https://service01.emedny.org:7602/MHService"), 
                                          ei, new AddressHeaderCollection());

mhsClient = new MHSClient( binding, ea );

mhsClient.ClientCredentials.ServiceCertificate.DefaultCertificate = 
    new X509Certificate2( // make the server certificate availble here );
mhsClient.ClientCredentials.ClientCertificate.Certificate = 
    new X509Certificate2( // make your client certificate available here );

mhsClient.ClientCredentials.UserName.UserName = "username";
// this is a password you  establish with eMedNy especially for this purpose
mhsClient.ClientCredentials.UserName.Password = "password"; 
mhsClient.ClientCredentials.ServiceCertificate.Authentication.CertificateValidationMode =
   System.ServiceModel.Security.X509CertificateValidationMode.None;

Transaction request = new Transaction();
request.transData = Encoding.UTF8.GetBytes( "270 message" );

Transaction response;
response = mhsClient.getEligibility( request );

string _271Message = Encoding.UTF8.GetString( response.transData );