If you want to plant this season, I would not incorporate the wood chips into the soil. Rake them off and save to use as a top dressing or mulch or to delineate pathways between the raised beds.

And mix together the topsoil and the more or less 'finished' compost thoroughly to fill the beds.....no layering :-)

You generally want the wood chips on the top of the soil. When they mix in with the soil their process of breaking down will compete with your plants for nitrogen. They "tie up the nitrogen" meaning the wood chips are hoarding the nitrogen temporarily and will release it as the chips finish composting. So, I'd rake the chips to the side, Spread out the compost and work it into the soil. Plant your plants then spread the chips back down. Studies seem to show that they don't mess with the nitrogen so much when they are on top.

But don't obsess about it, worst case scenario is they mix with the soil and you add a little nitrogen after your plants get established if they seem to need it.

In my more established beds I do layer. I brush away any old mulch from around the plants, put down a layer of compost, then a layer of mulch on the top. There are already plenty of worms and soil biome to move that compost down into the soil.

It is my understanding that only green wood chips affect the nitrogen level, and only if they are dug into the soil in sizable numbers. In this case, the chips are two years old, and it looks like most of them have decomposed already. You can certainly rake them off and reuse them, but if some end up in the soil, don't sweat it.

Where are you in NJ? I'm in Essex County, by Bloomfield/Montclair.

Wood chips don't hoard nitrogen. The bacteria and other microorganisms that feast on them do. Their microbial proteins contain that nitrogen, and those proteins are not useful nutrients for plants. When the food is gone, they die, and the nitrogen returns to the soil in usable form. This is true for any uncomposted organics that are dug into soil. If the chips are really already decomposed, no problem. Undecomposed organics are fine on top, because they aren't moist enough for the little beasties to form and suck up the nitrogen, and whatever is taken is taken from the top few millimeters only. Of course, they won't promptly decompose on top either.

Yes, as others have said the wood chips will go on the top, or rake them into their own pile on the side to decompose.

However, at the bottom of those chips you may have some rich black compost - go ahead and turn that into the soil as you dig in to create your raised beds. Add more compost at the same time. Just adding the amendments and air into the existing soil will probably raise it about five inches.