Landscape fabric is evil. When I first established my food forest, I used it liberally, laying it down on the ground all over the place and then piling wood chips on top of it. BIG mistake. First, the tree roots quickly entwined with the fabric making it very difficult to pull up later. Second, it effectively blocked all the carbon goodness of the mulch from being integrated down into the soil profile. Above the fabric, black crumbly humus. Below, grey and mostly lifeless clay. Several years later when I realized the mistake, I spent hours ripping that fabric loose from the fine tree roots and pulling it up. I'd laid hundreds of yards of that stuff. HUGE mistake.
Every now and then, I'll still find some piece of it out there and I'll try to pull it up. Its like digging your own grave. HORRIBLE stuff.
There is a difference between growing annual crops in traditional rows and beds (which most market gardens do for efficiency) and those of us using an integrated food forest approach. I don't think I've got a row of any one thing longer than 3 feet anywhere on my entire property—everything is plunked-down into little drifts and guilds throughout the orchard. On a limited basis, I've occasionally used black plastic as a surface mulch around some of the trees, to knockdown crab grass or other invasives that are hard to kill, but at the most, I'll only leave it there for 2 years. And, again, its on the surface, not buried. Plastic sheeting doesn't get tangled with the tree roots, and if you buy the good stuff, it's UV resistant so it doesn't crumble and fall apart after one summer of hot sun.
If you're not familiar with Stefan Sobkowiak's Miracle Farm in Quebec, he has created an integrated food forest that also functions as a you-pick garden.
http://www.permacultureorchard.com/the-farm/
http://miracle.farm/en/
https://www.youtube.com/watch?v=3riW_yiCN5E&list=PL-kCR5vVgbNFKf7ZJoPEzXg-UDJRU2uvb
He planted his trees according to the date the fruit will ripen, so that everything on one or two rows will all ripen in the same 10 day window—apples, peaches, pears, plums, cherries, etc. The next two rows ripen in the next 10 day window. Throughout the growing season, the trees ripen in succession, so that the customer can walk a set of rows within the orchard and fill their basket with everything ripe at that time. He uses black plastic to keep weeds down and retain moisture immediately beneath the trees, running the plastic along the length of the row, while letting grass grow in the alley between the rows. Then, he cuts holes in the plastic and plants annual veggies in that same space below the trees. He thinks this out well in advance of the tree ripening date, so that the veggies on that row are also ripe and producing at the exact window that the fruit is ripe. Thus, when a customer walks that row of trees, not only are the peaches, apples, pears and such ripe in the branches above, but below, they can find cabbages, carrots, tomatoes, etc. ready to pick beneath. It's quite impressive.
No two trees standing next to each other are the same. He's got hundreds of different varieties -- over 50 apples alone. Interspersed throughout are nitrogen fixers, berry bushes, and bee hives.
Once those rows are picked over and the last remaining fruit begins to fall to the ground, he cordons off those rows with electric fencing and runs sheep, chickens and ducks in to clean things up. Its a tremendously efficient system for the customers, the animals and to maintain, as every two weeks or so, you just move things over a row or two and open it up for picking or grazing. Nut trees ripen much later in the season (he's got something like 60 different varieties of nut trees as well) so he's able to open things back up to harvest the nuts. He's getting multiple yields off the system throughout the growing season.
Anyhow, here is a Permies thread that was moderated by Stefen where he talks about the use of black plastic in his integrated orchard. If you haven't read it, I think you'll find it interesting. (He's not an anti-plastic purist, the way some organic orchardists are.) He makes judicious use of plastic mulch.
https://permies.com/t/36586/Permie-Orchard-talk-plastic-mulch
Here is another thread where this topic was addressed:
https://permies.com/t/54409/Plastics-Permaculture-Weed-Control