Im having issue geting Complex JSON working as a parameter in my WCF Service.
Using, Microsoft.Net 3.5 SP1 in Visual Studio 2008 SP1
With the following Contract:
[ServiceContract]
public interface IService1
{
    [OperationContract]
    [WebGet(UriTemplate="GetDataUsingDataContract?composite={composite}", 
        BodyStyle=WebMessageBodyStyle.Wrapped, 
        RequestFormat=WebMessageFormat.Json, ResponseFormat = WebMessageFormat.Json)]
    CompositeType GetDataUsingDataContract(CompositeType composite);
    // TODO: Add your service operations here
}
// Use a data contract as illustrated in the sample below to add composite types to service operations
[DataContract]
public class CompositeType
{
    string boolValue = "true";
    string stringValue = "Hello ";
    [DataMember]
    public string BoolValue
    {
        get { return boolValue; }
        set { boolValue = value; }
    }
    [DataMember]
    public string StringValue
    {
        get { return stringValue; }
        set { stringValue = value; }
    }
}
Using the following URL:
http://localhost:1122/Service1.svc/GetDataUsingDataContract?composite={"BoolValue":"True","StringValue":"Hello"}
With the Enpoint Configuration:
<system.serviceModel>
    <services>
        <service name="WebHTTPBindingExample.Service1" behaviorConfiguration="WebHTTPBindingExample.Service1Behavior">
            <host>
                <baseAddresses>
                    <add baseAddress="http://localhost:8731/Design_Time_Addresses/WebHTTPBindingExample/Service1/"/>
                </baseAddresses>
            </host>
            <!-- Service Endpoints -->
            <!-- Unless fully qualified, address is relative to base address supplied above -->
            <!--<endpoint address="" binding="wsHttpBinding" contract="WebHTTPBindingExample.IService1">
                --><!-- 
      Upon deployment, the following identity element should be removed or replaced to reflect the 
      identity under which the deployed service runs.  If removed, WCF will infer an appropriate identity 
      automatically.
  --><!--
                <identity>
                    <dns value="localhost"/>
                </identity>
            </endpoint>-->
            <endpoint address="Web" behaviorConfiguration="ChatAspNetAjaxBehavior" binding="webHttpBinding" name="ajaxEndpoint" contract="WebHTTPBindingExample.IService1"/>
            <!-- Metadata Endpoints -->
            <!-- The Metadata Exchange endpoint is used by the service to describe itself to clients. -->
            <!-- This endpoint does not use a secure binding and should be secured or removed before deployment -->
            <endpoint address="mex" binding="mexHttpBinding" contract="IMetadataExchange"/>
        </service>
    </services>
    <behaviors>
        <serviceBehaviors>
            <behavior name="WebHTTPBindingExample.Service1Behavior">
                <!-- To avoid disclosing metadata information, 
  set the value below to false and remove the metadata endpoint above before deployment -->
                <serviceMetadata httpGetEnabled="True"/>
                <!-- To receive exception details in faults for debugging purposes, 
  set the value below to true.  Set to false before deployment 
  to avoid disclosing exception information -->
                <serviceDebug includeExceptionDetailInFaults="False"/>
            </behavior>
        </serviceBehaviors>
        <endpointBehaviors>
            <behavior name="ChatAspNetAjaxBehavior">
                <webHttp/>
            </behavior>
        </endpointBehaviors>
    </behaviors>
</system.serviceModel>
I Get the follwoing Error:
Operation 'GetDataUsingDataContract' in contract 'IService1' has a query variable named 'composite' of type 'WebHTTPBindingExample.CompositeType', but type 'WebHTTPBindingExample.CompositeType' is not convertible by 'QueryStringConverter'.  Variables for UriTemplate query values must have types that can be converted by 'QueryStringConverter'.
                [NEW ANSWER (2019]
In case somebody is still searching for this (I just did, and I figured out a good solution).
In contract file:
[OperationContract]
[WebInvoke(Method = "GET", ResponseFormat = WebMessageFormat.Json, UriTemplate = "TestBlockHeight?blockHeight={blockHeight}")]
Task<string> TestBlockHeight(BlockHeight blockHeight);
In service file:
public async Task<string> TestBlockHeight(BlockHeight blockHeight)
{
    return await Task.FromResult($"Called TestBlockHeight with parameter {blockHeight}");
}
My custom BlockHeight type class:
[TypeConverter(typeof(MyBlockHeightConverter))]
public class BlockHeight : IComparable<ulong>
{
    private ulong value;
    public BlockHeight(ulong blockHeight)
    {
        value = blockHeight;
    }
}
And the custom TypeConverter class that I needed to create:
public class MyBlockHeightConverter : TypeConverter
{
    public override object ConvertTo(ITypeDescriptorContext context, CultureInfo culture, object value, Type destinationType)
    {
        if(destinationType == typeof(string) && value is BlockHeight blockHeight)
        {
            return blockHeight.ToString();
        }
        return base.ConvertTo(context, culture, value, destinationType);
    }
    public override object ConvertFrom(ITypeDescriptorContext context, CultureInfo culture, object value)
    {
        if(value is string str)
        {
            return new BlockHeight(ulong.Parse(str));
        }
        return base.ConvertFrom(context, culture, value);
    }
    public override bool CanConvertFrom(ITypeDescriptorContext context, Type sourceType)
    {
        if(sourceType == typeof(string))
        {
            return true;
        }
        return base.CanConvertFrom(context, sourceType);
    }
    public override bool CanConvertTo(ITypeDescriptorContext context, Type destinationType)
    {
        if (destinationType == typeof(string))
        {
            return true;
        }
        return base.CanConvertTo(context, destinationType);
    }
}
This works because WCF uses a QueryStringConverter to serialize url parameters, and only specific types are allowed. One of these types is an arbitrary type which is decorated with TypeConverterAttribute. More info here:
https://docs.microsoft.com/en-us/dotnet/api/system.servicemodel.dispatcher.querystringconverter?view=netframework-4.8
I don't believe you're allowed to pass complex types on the query string using WCF this way. See this response from a Microsoft tech in the ASP.NET forums - it's similar to your situation.
Based on how you've stubbed out your service method, it seems like a more appropriate verb to use would be POST or PUT, and you could put your CompositeType payload in the request body.  But I'm guessing as to your intention.
I was able to make your code work and still use a GET by changing the query string type from CompositeType to String and then deserializing the JSON string into a CompositeType by using the ASP.NET JavaScriptSerializer class.  (You can use your favorite JSON helper class here -- I'm partial to JSON.NET, but I also hear FlexJson is very good, too.)
I didn't touch your web.config (except to make it work in my local test app). My only change was in the service method signature and the implementation of the service method.
[ServiceContract]
public interface IService1
{
    [OperationContract]
    [WebGet(UriTemplate = "GetDataUsingDataContract?composite={composite}",
        BodyStyle = WebMessageBodyStyle.Wrapped,
        RequestFormat = WebMessageFormat.Json, ResponseFormat = WebMessageFormat.Json)]
    CompositeType GetDataUsingDataContract(String composite);
    // TODO: Add your service operations here
}
public class Service1 : IService1
{
    public CompositeType GetDataUsingDataContract(String composite)
    {
        //use the JavaScriptSerializer to convert the string to a CompositeType instance
        JavaScriptSerializer jscript = new JavaScriptSerializer();
        CompositeType newComp = jscript.Deserialize<CompositeType>(composite);
        newComp.StringValue += " NEW!";
        return newComp;
    }
}
I hope this helps. Let me know if you have other questions with this.
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