I have dealt with this stuff and unfortunately your husband is right. My neighbor finally took it out and I am still digging up root-stems I didn't know were growing under what was front lawn (now all 'cottage'). It's been almost a year and shoots still appear next door.

I think it should be banned. That's how much I hate it.

It is banned here and in Washington but people still plant it.

Yes, it will come through a wood fence, my neighbor's did for years.

Round up is only marginally effective on it but I did stand on a ladder and spray it over the fence for years and it has finally died. So has the bindweed in the other neighbor's.

Round up does not harm the soil and does not transfer through the soil. You have to hit the foliage for it to work.