I have a semi woody bed thing going on at the moment. When I moved into my house, there was a bit of a play area covered in gravel and a sand pit, etc... for the children of the previous owner. I turned the sand pit into a chicken yard, and put 8 6'x'4 raised garden beds in for growing vegetables (I have perennials, herbs, etc... in separate, in-ground beds). When it came time to fill them with top soil, it would have cost about $500, which would have sucked pretty hard. Luckily, when I was down at the local rubbish tip, I saw that they offered composted green waste for $10 a trailer load. whilst the smaller leaves and whatnot had turned to rich dark humus, the larger branches that had been mulched still existed as wood chips. The effect is about a 50/50 mix of wood chips and composted soil. The wood chips act like my woody bed sponges, and they work to fantastic effect. As a bonus, it meant that I only had to pay $40 for soil instead of $500.
I have my beds set up on PLC based irrigation, which is actually fantastic. I put micro sprinklers on 4 times a day for 3 minutes. The 2 cycles during the middle of the day, whilst its frowned upon, only uses a couple of liters of water, and it protects my plants from wilting during the day in the middle of summer (it gets pretty hot in Australia).
I like the cardboard mulch, does it ever dry out and go hard? I'm a big fan of sugar cane mulch, myself.