DH and I disagree about ours/neighbour fence ...opinions please

[spacepoppers]

So, our garden backs onto the bottom of neighbours garden. We have a shortish fence, which is dilapidated, neighbour has a taller fence which is equally dilapidated. There is about a foot gap between the two. Neighbour suggests that we do away with both fences, and we both contribute to the cost of one new fence.
This makes sense to me, as currently we're both looking at an eyesore, but DH disagrees, abd says we shouldn't contribute to a fence that technically isn't ours and that we won't be allowed to paint etc without their permission.
Opinions please wise Mumsnetters!

[recycledteenager24]

check your title deeds, this is probably a shared boundary fence and you both own it

[LaurieFairyCake]

But you can agree to paint it and maintain it if you both agree

Im not suggesting you pay for their fence without doing so - I'm guessing that's where he's coming from?

[spacepoppers]

Oh, I will definitely check. If that's the case, and we share it, that would make sense then to do away with both our separate fences and have a shared one?

[user3274826]

Why wouldn't it be half yours? You can paint your side as you wish and it will be 50% of the cost of what you would pay otherwise. I can't see why he'd have an issue with this.

[StoneofDestiny]

You want a fence, pay for half.

[Keepmeawayfromthebuffet]

I agree with you, should pay for half