You have a couple options here. The green screen interfaces you're referring to is the IMS Message Format Service (MFS) which will take the green screen inputs and map them to the inputs for an IMS transaction.
The easiest solution which requires paid tooling would be the IMS MFS SOA solution. This will take the green screen interface files (MFS maps) and generate an equivalent servlet for you that you can apply a CSS style sheet too and deploy into a Java application server.
If you would prefer to have more flexibility in how you design your web front end, then you can take advantage of a few other IMS solutions that basically invoke an IMS transaction remotely through TCP/IP and incorporate that into your web application code:
- z/OS Connect - IBM's REST gateway for most z/OS assets. This will allow you to invoke IMS transactions, CICS transactions, and Db2 stored procedures as a REST service.
- IMS SOAP Gateway - This will allow you to invoke an IMS transaction as a SOAP service. I wouldn't recommend it however as IMS has stabilized the product meaning there will be no new enhancements.
- IMS TM Resource Adapter - This is a fairly straightforward API that's meant for JEE deployment. It takes advantage of the security and connection pooling features you would expect of a JEE resource adapter.
- IMS Connect API for Java - This is a bare bones Java API. You'll be responsible for constructing the input payloads and interpreting the output of the IMS transactions.