The two main purposes of a DI, as far as I'm concerned:
Impedance matching: TS has an insanely promiscuous input stage (so you might as well throw your ultra-high-impedance gizmos before it) and an output impedance below 1K. You can further lower this with a little tinkering. If I remember correctly, the impedance lowering stays in effect even if you bypass the pedal through its own switch... this is why a bunch of wankers spend $50 to ruin their pedal with a stupidly big switch sticking out the top unnaturally and jerk off to the phrase "true bypass", but that's not at all necessary - or even recommended. Long story short, your impedance is already well handled by the pedal as soon as you plug it in - whether you activate it or not - so if all you need is impedance matching, you might not need a DI.
Balancing output: TS has an unbalanced output. If you used a DI, placing it before the TS would get rid of that perk immediately.
From this, I'd put the TS before the DI, if anywhere. If your interface's input is fine with an impedance of ~1K and the balancing act doesn't concern you, don't worry about it at all.
Jeff