Using Apache POI is relatively easy to do. So we can use NPOI to do the Transform in C#.

Using as a basis this answer of Convert word to HTML with Apache POI

Java version

HWPFDocumentCore wordDocument = WordToHtmlUtils.loadDoc(new
FileInputStream("D:\\temp\\seo\\1.doc"));

WordToHtmlConverter wordToHtmlConverter = new WordToHtmlConverter(
        DocumentBuilderFactory.newInstance().newDocumentBuilder()
                .newDocument());
wordToHtmlConverter.processDocument(wordDocument);
Document htmlDocument = wordToHtmlConverter.getDocument();
ByteArrayOutputStream out = new ByteArrayOutputStream();
DOMSource domSource = new DOMSource(htmlDocument);
StreamResult streamResult = new StreamResult(out);

TransformerFactory tf = TransformerFactory.newInstance();
Transformer serializer = tf.newTransformer();
serializer.setOutputProperty(OutputKeys.ENCODING, "UTF-8");
serializer.setOutputProperty(OutputKeys.INDENT, "yes");
serializer.setOutputProperty(OutputKeys.METHOD, "html");
serializer.transform(domSource, streamResult);
out.close();

String result = new String(out.toByteArray());
System.out.println(result);

We transform this to C #

HWPFDocumentCore wordDocument = WordToHtmlUtils.LoadDoc(@"D:\Hola.doc"); 

WordToHtmlConverter wordToHtmlConverter = new WordToHtmlConverter(
    new XmlDocument());

wordToHtmlConverter.ProcessDocument(wordDocument);

XmlDocument htmlDocument = wordToHtmlConverter.Document;

htmlDocument.Save(@"D:\Hola.html");

I recommend that do not download NPOI by nuget (current version 2.2.1) and use version 2.1.3.1 but from the official page since two more files are needed which do not come in NuGet NPOI.ScratchPad.HSSF.dll and NPOI.ScratchPad.HWPF.dll both compiled with NET Framework 2.x Y needs the other libraries to be version 2.X too. These 2 files can be downloaded from npoi Github

By testing it seems that the npoi version has a bug in the end result of the HTML, since to simulate the format it creates the style with the first letter of the tag type and an incremental number

<!-- ejemplo POI java-->
span.s1{color:red;}
...
<span class="s1">Hola</span>

But for some reason the NET version does not generates them well

<!-- ejemplo NPOI C#-->
span.s1{color:red;}
...
<span>Hola</span>

Maybe it has to do with Transformer but I don't know what the equivalence will be in C #

By doing a manual count, you may no longer need to make the output look good

    ....
    XmlNode node = htmlDocument.FirstChild.LastChild; //encontramos el body
    EditNode(node); //metodo de edición recursiva
    htmlDocument.Save(@"D:\tmp18\Hola.html");
}

Dictionary<string, int> cuenta; //para llevar la cuenta de cada elemento

private void EditNode(XmlNode node) {
    try
    {
        XmlElement xe = (XmlElement)node;     

        xe.SetAttribute("class", cuenta[xe.LocalName].ToString()); //localName seria span o p por ejemplo
        cuenta[xe.LocalName] += 1;
    }
    catch (Exception) { return; }

    if (node.HasChildNodes) {
        foreach (XmlNode x in node.ChildNodes) {                
            EditNode(x);
        }
    }

}