You could use insert cables (TRS to 2x TS), with the TRS plugged all the way into the insert points. The send (the Tip signal on most any newer board) will go to the interface input. Set the interface to monitor its inputs on the corresponding outputs. Use the cable's return to connect to the outputs of the interface, which will route the signal back into the mixer's signal path. You'll be able to set up your own submix with the faders and it won't affect the recording levels.
This is, of course, if you don't trust the "half-way in" method, or if you have an older board where the insert send is on the ring instead of the tip (my Allen & Heath is like this). The reason the the half-way in works without interrupting the signal flow is because the tip is normalled to the ring in the insert, so that when there's nothing plugged in the signal passes through. Inserting a cable all the way in breaks the normal, and since you don't have a return signal on the ring connector, there's nothing to continue through the rest of the signal path. If you only go halfway in though, the tip of your TS cable is touching the ring's connector, which is normalled to the tip. Since the normal isn't broken, the tip in the insert point normals to the ring, which is also touching the tip of your cable, in effect multing the signal to both the rest of the mixer's signal chain and out through your cable.
If your board is wired with the send on the ring, clicking halfway will tap into the send, but will also break that normal, so you'll only get signal on your cable and not through the mixer. Pushing the cable all the way in, though taps your tip into the ring, but since the normal is broken, the ring isn't seeing any signal, so your cable sees no signal. You would need to make special TRS connectors that re-connected the tip and ring if you wanted to have signal on both your cable and your mixer's signal path. It took me a while to figure out why it didn't work, before I realized my console was wired opposite of AES standards now. Fortunately I have buss outputs so I don't need to worry about tapping into insert points.