The Roku connects to your television and then the headphones can connect to the television. If the headphones work now with whatever program sources you are using then they will also work with programming fed from the Roku. The Roku unit itself does not have a headphone jack and whatever audio features the TV is equipped with will still be functional.
Just read this on another post. Haven't tried it yet: "...we had the same problem. We finally resolved it by connecting the Roku to the TV via HDMI cables, and then using the A/V cable that came with your Roku, connect that from the Roku to your headphones using two of the connectors but not the yellow one. You'll need to get two female RC connectors so the two ends of the A/V cable and the headphones receiver connectors will connect."
I must have something hooked up wrong because my Roku does not work with my Sennheiser RS120 Headphones. I hear my TV fine but hear nothing that is Roku related. Can I do something differently? Do I need a blue tooth bridge? I would love a solution.