How are the roads from Luxembourg to Interlaken?

You can go either via French or via German freeways. The French freeways are like US turnpikes. The German freeways are built for speeds above 100 mph. Taking the French freeways is a bit shorter in total miles. And the drive without any breaks should take you 6 hours... so probably 8 hours including comfort breaks.

Driving the German route would take you along A5 south of Karlsruhe. Although I haven't driven along this stretch of Autobahn since late summer, at that time there was an insane amount of roadwork. Almost as much length of road under renovation as not. Avoid this route if you can.

I drove this route in September, and have taken several variants over the years (I tend to drive it at least once a year). The French autoroute on the route Luxembourg = Metz = Strasbourg = Colmar = St Louis (cross into Switzerland) = Basel = Bern = Spiez = Interlaken is fast, mostly 3 lanes each way (watch out for cameras and tolls) and easy. Not terrifically scenic on the autoroute but mostly 130kph that can be achieved. The German autobahn route Luxembourg = Trier = Saarlouis = Karlsruhe = Freiburg-i-B = Basel (cross into Switzerland) and as above, is mostly 2 lanes each way, is typical German autobahn. That means it winds from time to time, can be very fast in bursts, can just a quickly come to a grinding screeching halt (with or without accident) (causing or not causing accident) and absolutely creeps along or just stops at construction sites and contraflows (that's an English expression, I don't know the German or American translation - it means that one or more lanes cross over to the other direction roadway while the other direction goes over to the shoulder and perhaps one lane). Learn the German word "stau" which is the German equivalent of a tailback or traffic jam. They tend to arise suddenly and frequently mean a complete stop for some time. On the traffic reports you will hear the location, direction, number of kilometers length of the stopped traffic, and the word "stau". This year it wasn't too bad south of Freiburg-i-B, not very good Karlsruhe to Baden-Baden, not good Baden-Baden to Freiburg-i-B. You could also go Luxembourg = Metz = Nancy, then leave the autoroute and go over the Vosges mountains direct to Strasbourg or Colmar. That route was interminably slow when we did it. There are also other possible routes.

I much prefer driving on the French side to the German side. As others have mentioned, that section of the A-5 in summer has a lot of road work going on. The two-lane parts of the Autobahn are not fun, because you're either stuck going 50 mph behind lots of trucks, or you have to gun it to over 100 mph to pass on the left. It's very "active" driving and not relaxing at all. When I found a route home from Strasbourg that allowed me to stay on French highways for a lot longer it was heaven - much more like driving back in the U.S.