You are using a chemical fertilizer and its not recommended for any herbs or edibles. The use of natural fertilizers is better for most plants. Things like fish emulsion and seaweed concentrates can help a lot. Usually herbs don't need much in the way of fertiizers, but using a raw chemical product like Urea is very bad. Plants will yellow if watered too much. They can also lack iron in the soil, but that condition is less common. Look for organic fertilizers when feeding plants. Avoid things like Miracle Grow and other chemicla bsed ones that are just plain bad for edible plants and herbs.

As Ksrogers said, 'herbs don't need much in the way of fertilisers' - most of the common culinary ones, anyway. I find the very best of all fertilisers is compost. Just ordinary household compost, a handful or two around the plant once every blue moon or so (perhaps a little more often if the plants are in pots- it's a good potting mix topper-upper). You can buy it from your garden centre in bags if you haven't got your own compost heap.

Certainly, you should never fertilise baby plants, or those which have just been transplanted. It's too easy to overdose them!

Killing by kindness is the most common mistake made by beginner-gardeners.

Using bagged compost at best may provide many things that are not safely broken down yet. I would mix the bagged compost with a bit of peat moss and moisten slightly and then cover it loosly and allow it to break down further, about a month. Doing this will give a safer product. I used bagged compost added to my potato soil and it introduced wire worms to my growing potatoes. They were pierced all over with tiny pinholes that went ito the flesh an inch or so. Turns out the compost was not fully broken down yet, Thats why I mentioned fish meal and seaweed. As to losses, the plants are gone, if they have been 'burned' by too much Urea. Start with new soil and don;t add any fertilizers. If your seed starting, its best to use a STERILE soilless medium (shreadded coconut husks- coir). These mediums are lighter and looser, so they allow seeds to germinate and form roots early. The sterile medium also has no bacteria or harmful things that can cause damping off or other malady.

You may want to check for root pests. My parsley was killed by termites. Parsley produces a woody tuber that termites found irresistible. In this termite-infested area, the only way to grow parsley is in a pot, away from soil access. The symptom was the same as your description, the leafs turn light green, and the plants melted and died.

And yes, never use urea. It is a very bad fertilizer. Good for first year only. Over time my garden soil is turned into a hard clay.

A better choice for the garden as a nitrogen boost is nitrate of soda. Much less powerful and breaks down much faster. This year, I have to add that to my garden soil before I do my tilling, but I also add the fish meal and feather meal for long term nitrogen. We have termites too. They chewed through a piece of 2x4 I left on the ground. It didn't take long to make it into Swiss cheese.