Проблемы HTTPS в лазурном

Я подписался на проект, которым вы поделились в комментарии, он работает на моей стороне.

web.config

<?xml version = "1.0" encoding = "utf-8"?>
<!--
     This configuration file is required if iisnode is used to run node processes behind
     IIS or IIS Express.  For more information, visit:

     https://github.com/tjanczuk/iisnode/blob/master/src/samples/configuration/web.config
-->

<configuration>
  <system.webServer>
    <!-- Visit http://blogs.msdn.com/b/windowsazure/archive/2013/11/14/introduction-to-websockets-on-windows-azure-web-sites.aspx for more information on WebSocket support -->
    <webSocket enabled = "false" />
    <handlers>
      <!-- Indicates that the server.js file is a node.js site to be handled by the iisnode module -->
      <add name = "iisnode" path = "app.js" verb = "*" modules = "iisnode"/>
    </handlers>
    <rewrite>
      <rules>
        <!-- Do not interfere with requests for node-inspector debugging -->
        <rule name = "NodeInspector" patternSyntax = "ECMAScript" stopProcessing = "true">
          <match url = "^app.js/debug[/]?" />
        </rule>

        <!-- First we consider whether the incoming URL matches a physical file in the /public folder -->
        <rule name = "StaticContent">
          <action type = "Rewrite" url = "public{REQUEST_URI}"/>
        </rule>

        <!-- All other URLs are mapped to the node.js site entry point -->
        <rule name = "DynamicContent">
          <conditions>
            <add input = "{REQUEST_FILENAME}" matchType = "IsFile" negate = "True"/>
          </conditions>
          <action type = "Rewrite" url = "app.js"/>
        </rule>
      </rules>
    </rewrite>

    <!-- 'bin' directory has no special meaning in node.js and apps can be placed in it -->
    <security>
      <requestFiltering>
        <hiddenSegments>
          <remove segment = "bin"/>
        </hiddenSegments>
      </requestFiltering>
    </security>

    <!-- Make sure error responses are left untouched -->
    <httpErrors existingResponse = "PassThrough" />

    <!--
      You can control how Node is hosted within IIS using the following options:
        * watchedFiles: semi-colon separated list of files that will be watched for changes to restart the server
        * node_env: will be propagated to node as NODE_ENV environment variable
        * debuggingEnabled - controls whether the built-in debugger is enabled

      See https://github.com/tjanczuk/iisnode/blob/master/src/samples/configuration/web.config for a full list of options
    -->
    <iisnode watchedFiles = "web.config;*.js"/>
  </system.webServer>
</configuration>

Если вы поместите index.html в общую папку, созданную вами непосредственно в wwwroot/, вам необходимо добавить в свой код приведенный ниже код на основе этого статья.

app.use(express.static('public'))

Я тестировал это.

Обновить ответ:

Я также включаю опцию Web Sockets.