How do I determine left and right side of a line (linear road network), with that determine the side of the road Zip Code boundaries are on?

I am dealing with TomTom data. I am updating the zip code information from a more reliable source. The reliable zip code source does not contain Left or Right for zipcode, it is instead just polygon boundaries with one zipcode. My issue is trying to figure out which side of the road these boundaries are on (Left or Right) and then applying that result to the TomTom road data as ZipCode_L or R. The images below show a zoomed out shot of my data and a zoomed in shot with the Road circled that this situation would pertain to. Red outlines are the Zip code boundaries and the Lime Green lines are the Roads.