You pose an interesting question.
One antenna (your transmitting/receiving antenna) is vertically
polarized; the tv antenna is horizontally polarized. Normally, a
ground plane is formed by wires running away from a vertical antenna -
or - a mesh of wire extending away from the antenna.
Since neither exist, I suspect you would have little coupling to the
tv antenna. The horizontal elements are so short that I doubt any
directly beneath the vertical would have an effect and the boom might
have a small effect, but only in the directions that it is running
beneath the vertical.
I'm not saying there is no effect; I am of the belief that any effect
would be exceedingly small (with a possible exception of a small
change in the radiation pattern in the direction (both ends) of the tv
antenna.
The best solution is to convince your wife that you need an 8 element
rotatable cross-polarized lightning deflector mounted on top of a 120
foot tower

)
(can we spell 'Yagi'?) LOL
(why do I see a number of the group planning to try and convince their
wives that they need a similar 'lightning deflector'?)
73 from Rochester, NY
Jim