Answer: English ivy (Hedera helix) is an extremely tenacious plant and I would not expect a layer of mulch to kill it although it might take it some time during the growing season to pop back up through the the mulch.
This ground cover is deeply and widely rooted and could easily outcompete newly planted shrubs and flowers. It will also spread aggressively and climb over top of neighboring plants and could smother new plants. Consequently, I would suggest you plan on eradicating the ivy prior to planting new things in that area.
You might be able to do the job using an herbicide containing glyphosate, however this must be applied according to the label instuctions paying particular attention to the temperature and coverage requirements. In order for it to be effective it must also be applied when the plant is actively growing, so you would have to wait for the ivy to begin growing again this summer. (You might be able to speed it up by raking aside the mulch to allow the sun to reach the ivy.) In the meantime, you might want to check with your county extension and see if they have any other suggestions as to what to do prior to planting.
With regard to wood chips in general, it is a good idea to make sure they are well aged (about a year old or even longer) prior to using them as mulch, and they should be placed (as with any mulch) so that they do not contact the stems or trunks of your plants. For mulch purposes a layer about two inches deep year round should be sufficient.
Finally, it might be worthwhile to carefully evaluate the area before removing the ivy permanently. Sometimes ivy is used as a ground cover where the growing conditions are difficult and little else will grow in that spot. Excess shade, poor or compacted soil, a steep slope, runoff problems, competing tree roots, or similar factors can make it difficult to establish a landscape planting. Ivy is often used in such difficult situations because it is a very resiliant plant and can survive under adverse conditions; it is possible that your ivy was originally planted to solve a rather difficult problem. So on a conservative note, I would suggest you might want to consider this possibility, perhaps in consultation with your county extension, prior to eradicating it -- it would be a shame to go through all the time and effort and trouble to try to get rid of it only to realize later that it wasn't such a bad choice for the location.
On the other hand of course it is possible it has simply become overgrown and needs to be controlled, so good luck with your project whichever way you decide to go with it.
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