I’ve only ever investigated getting a studio subwoofer into my system. The way that would work is you would take the two TRRS / XLR plugs out of your monitors, and then connect them to the Sub’s inputs. You would then run the L & R output from the subwoofer into your monitors. So the subwoofer would handle the entire signal coming out of your interface, and then handle what is playing through the sub and the monitors. In fact, studio subs would let you control the crossover frequency. This means you would control what frequencies are going to play through the subwoofer, and which frequencies you would hear from the monitors. You would also get to control the overall level of the subwoofer as well as the phase.
For your situation, you have to see whether the subwoofer you’ve got is passive or active. If it doesn’t connect directly to an electrical outlet, it’s a passive subwoofer. In that case it’s going to be really hard to put it into your setup. You’ll need a separate amplifier for it. If it does connect to an electrical outlet, it’s an active subwoofer, with a built in amplifier. But generally home cinema systems use passive speakers for the L & R’s, so again, depending on your monitors you may get something or nothing by plugging your monitors into the subwoofer.
Now, the only way I could think of avoiding all of this hassle, would be to connect the subwoofer to the interface alongside your monitors. But in this case, you’d be routing your audio from your DAW into 2 monitors, and then the subwoofer. So essentially all frequencies would be sent to all three speakers. I think that defeats the point of having the subwoofer in the setup, but I could be wrong about this.
I think I’ll let somebody who actually has a subwoofer in their setup take over from here…