In JSP I can share HTML code by using include:
<jsp:include page="subsection.jsp" >
For the life of me, I can't tell how in ASP.NET I should be including shared HTML. I could use a template control, but this really isn't the same thing. I could use a site master page and content placeholders, but this also is not the same and requires a different approach to developing my pages.
Am I out of luck or is there a function in ASP.NET similar to JSP's include?
You will have to enable it from the server then only you can use include html files.
Instructions to enable SSI in IIS7 are available at http://tech.mikeal.com/
For dynamic content, there is a built-in method of templating called MasterPages, this should be used instead.
I think what you are wanting can be accomplished in Asp.Net through User Controls. If you were in Asp.Net MVC you would want to use Partial Views.