You can convert HTML file to DOCX stream (byte array etc) by using following C# Code of Aspose.Words for .NET API:
Document doc = new Document("E:\\Temp\\in.html");
MemoryStream stream = new MemoryStream();
stream.Position = 0;
byte bytes = stream.ToArray();
After that you can upload the DOCX stream or byte array to SharePoint’s Document Library. Of-course, you do not need Aspose.Words for .NET to push files to SharePoint’s Document Library. Instead, Microsoft provides an API for that in Microsoft.SharePoint namespace.
For example, you can use SPFolder.Files.Add() to add a file. An example here: SPFileCollection class might be helpful.