When Martha says she learned from the best and Ten gets a big head and goes “Weeeell,” all I can think of is River telling Eleven she learned to fly the TARDIS from the very best and then him going, “Well, yeah,” and then her saying it was a shame he was busy that day.
First, it would go against the “every female companion (except for Donna) has to fancy The Doctor” cliche (maybe we could even get away from the “every female companion must kiss The Doctor” cliche too) and it would just be downright hilarious to see The Doctor jealous over the fact that his wife is flirting with his companion.
I saw a Doctor/Rose fic the other day called You Watch Us Run.
Just, no.