I think that the decomposition process works much slower in the winter than the summer, so I'm not particularly surprised your mulch is still breaking down. What was your mulch material - leaves, wood chip, other organic matter? Different materials will obviously break down at different rates.
It depends also on what sort of weeds you had underneath - persistent perennial weeds like bindweed or creeping thistle will probably come back and stronger tap rooted ones will punch through several layers of cardboard here quite happily

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I think like Christopher I'd be inclined to see if I could get more compost and maybe cardboard. Charles Dowding puts about 6 inches of compost down to smother his weeds (although I don't think he uses cardboard) so the thicker the layer the better (particularly with clay soil). Maybe you could rake some of it up to make a thicker layer on part of it and plant early crops in that, and work on building up the rest of the area for later planted seeds. If the mulch really is rather woody then more compost on top or possibly adding more nitrogen rich material (like grass clippings, coffee grounds, urine..) first to help break it down more quickly. It's early spring yet, so I wouldn't panic.