I've been mulching with black plastic for many years now. The trick to watering is to run a soak hose/ weeping hose under the plastic and about 8-10 inches from the plant stem.
I put out a 12-inch round, 1-inch deep dish, ran the soak hose over it, and timed how long it took to fill with water. If my area doesn't get the usual 1 inch a week rainfall then we hook up the hose and set the timer to make up the difference.
The plastic keeps evaporation down, keeps the weed seed from sprouting, and makes a nice edge to mow over - no flying wood chips, no molding leaf matter to set off my allergies.