How to configure WCF services to work through HTTPS without HTTP binding?

you need to use mexHTTPSBinding unstead of mexHTTPBinding

<endpoint address="mex" binding="mexHttpsBinding" contract="IMetadataExchange" />

Modify your configuration this way:

<behaviors>
  <serviceBehaviors>
    <behavior> <!-- behavior can have name (must have name in WCF 3.x) -->
      <serviceMetadata httpGetEnabled="false" httpsGetEnabled="true" />
    </behavior>
  </serviceBehaviors>
</behaviors>