Hm, that's funny. It's the same with Luke and I - the games change around, and the characters do as well. Popular are [some character from the movie Cars] and Luigi (with me as Luigi - a character from that movie); variants on Winnie-the-Pooh stories, with me often filling multiple roles; characters from Monsters, Inc. in wildly random configurations; characters from Dora the Explorer, also in wildly random configurations; characters from Thomas the Tank Engine.
A theory that I'm making up and exploring as I type this post is that the more familiarity Luke has with the source material, the more set the game parameters are. Frequently the Winnie-the-Pooh games involve Tigger and Eeyore meeting Winnie-the-Pooh for the first time (this improv is most assuredly Not Canon...), for instance, while the Dora games are pretty free-form.
Also, a number of these games involve playing with toys, so they're almost puppetry improv, and not simply improv. That doesn't work so well in the car, though, where these scenes frequently take place.
As an aside, when I was small, my usual daddy-time interaction was improvised stories, along the lines you described a couple years back with Aviva. One of the recurring characters in these stories, oddly enough was Stinkyfeet, who I believe was my avatar, but I could be recalling incorrectly...
Good to know I'm still up to no good ;)