No, they won't, provided you don't pile up the mulch against the trunk of the tree - leave that clear by a good 2 inches all round. Not sure what you mean by black woven plastic sheet - hopefully you mean the geotextile fabric sold generally under the title 'weed fabric' and not actual plastic. Make sure the ground is moist when you add the mulch and fabric though. Alternatively, you could just use mulch on its own, specially if there's a need to add feed to to the soil around the trees (difficult with a membrane in place) - 2-3 inches deep should dramatically reduce weed germination. Best applied in spring - within a month weeds won't be germinating anyway at this time of year.

Ta for that. I was going to use the black woven membrane
As I have a 100m roll of same. The stuff the commercial greenhouses use. Will take your advice!