As @MichaelT pointed out, the overall architecture of an ASP.NET and J2EE application are basically the same. J2EE applications don't have to be big huge Java applications, you can whip something up in a few hours that works quite well and can be deployed.
The earlier implementations of J2EE were terrible and clunky and involved loads of XML configuration to wire up components of the application but that isn't the case any more. The canonical J2EE framework is Spring and its associated packages. With Java 1.5+ you can use annotations in lieu of configuration files and other tools and frameworks (e.g. Maven) make dependency management rather simple. I won't go into which tool/framework is better/worse here as (with all other things) they each have their place.
I found this link which provides a decent comparison of ASP.NET and J2EE and basically says they're the same. Which means you will be creating a bunch of JSPs and Servlets, that's what a Java web application is.
In terms of "what design do I follow?" my suggestion is to refactor/redesign your implementation when porting over to Java. Use things such as Spring, Hibernate, etc. if you're not already using the .NET equivalents. It isn't often you get a chance to redevelop a legacy system in a new language - so take the opportunity to improve it.