Have you considered the WinHTTP API or the WinHTTPRequest Object?
This was designed as a server technology, and is much more robust than WinInet. It has some limitations however: it requires NT4 & IE 5.01, or else Win2000 (which includes IE 5.01 or later).
To use SSL you'll need a client certificate, but you might be able to "borrow" IE's from the client machine's local certificate store. I haven't tried this.
While meant as a "server side" technology, this doesn't mean you can use it to create an HTTPS server. It was designed to allow server-side logic at the web server to perform "client" actions against a second server. SOAP transactions, "web scraping" and so on. In other words your web server was to look like a browser to a second web server. In other words, there's nothing like a Bind or Listen method.
I'm pretty sure this is about all it can be used for. It wouldn't offer something like an SSL version of a raw TCP socket for general-purpose communication. It only does HTTP/HTTPS.
You'd use this to build a browser from scratch for example, or maybe a client that acts like a browser (from the server's poit of view) but does something else, like web crawling or HTTP file downloads. Or a custom client that interacts with a server using SOAP.
You didn't give specifics, so I can't say whether it might meet your needs.
See