Assuming you have the ability to manage the server configuration, why not have the separate process generate log entries via syslog, then use a simple server-side script to examine the log entries thus generated, and present them in the browser in whatever fashion you find most useful? Syslog already is a "universal message broker", after all, and it's almost always easier to make use of an existing capability than to develop a new one from scratch.
Unfortunately, I'm unable to present a really specific answer, because you haven't identified the server-side language you're using; if you'll edit your question to include that information, and comment on my answer to let me know you've done so, I'll see what I can come up with to give you a real start on solving the problem.