I suppose it depends how much work you want to do. You could remove the edging and replace it and it's likely staked down so maybe that's why it doesn't move so easily. Or get some more river rock and pea gravel to replenish the bare areas to clean it up. I'll bet all those rocks look pretty when they get wet!

I assure you that your husband does not think that looks fine. I'm sorry that his solution is to dismiss your legitimate concern. This is also creating a problem for your neighbor. It looks bad and it makes both lawns hard to mow.

One solution is to take out the creek bed, add soil to make the divide as level as possible with the lawns, and plant a strip of shrubs or ornamental grasses. Use the rocks to make a cohesive rock garden between the properties at the sidewalk.

Another possibility is to remove some rocks to narrow the creek and give you better access to address the edge problem. It might also allow you to have a mulched area to separate the lawn from the rock. You can't cut back your lawn any further to create a mulched area--you can only make the creek narrower. It could then flare out more naturally at the sidewalk by incorporating some of your neighbor's bed. Make this a shared bed by removing the pointless left edging strip, moving some rocks over, and selecting complementary plants.

Is is a functional dry creek? If so, how well or poorly is it currently functioning?

Have you lived there long enough to see if it is helpful when it rains for drainage? There are other ways to accomplish good drainage in any case. If it were me I would want to remove it (I don't find it to be attractive at all), but you will have to decide for yourself if you think it has any redeeming qualities. I'm sure DH just doesn't want to deal with it. It may not be easy to find someone to take away that quantity of rock, but I agree with you, you can't leave it looking the way it does now.

The easiest way to deal with it is to plant stuff between the fabric and the edging.

Lift all the rock, lay several inches of crushed gravel for drainage, replace rock.

Like a dry creek bed or even live creek beds, it has been eroding since the day after it was built and will only continue to do so.

Obviously it is serving a function. Both yards slope towards it and it is carrying the runoff from at least one downspout. Could do with a bit of tidying up. Reset the edging and reposition the irrigation & add a bit more rock to cover the tubing.

@beesneeds - I do not think it’s a functional dry creek. And @kandrewspa - you are correct, DH doesn’t want to deal with it right now. We do have other updates going on. @Eileen - I like your suggestion of creating a rock garden instead. Our home is part of an HOA and there are so many rules! Whatever I do, I’ll have to get approval from the board, which means I will need to show them a plan.

Maybe this is too complicated for me to DIY?

It looks like it was designed specifically for the downspouts on that side of the house to drain out to the sidewalk. It sounds like you're not sure if it does or whether it functions as such in a downpour.

What I would do? Arrange some of the larger rocks along the benderboard, so as to hide it and also to hold down the fabric.

Here's some inspiration for a more natural creek bed. The lawn is incorporated as part of the bed and creek bed. Unlike your lawn, it doesn't have a rigid edge and shape not found in nature. You could do a narrower version of this. Maybe the top of the rocked area would only need to be 12-18" wide. It would widen as it moves toward the sidewalk. Plants would help remove the rigidity too.