Dear Marta,

Thank you for contacting us about leaf miners in your vegetables. They are cyclical and there is no way to get rid of them permanently, but damage they cause is primarily cosmetic and can often be controlled by prevention and cultural methods. 

An Extension article states:

Weed control and crop rotation are the first line of defense, since these leafminers feed mostly on one crop group that also includes many common weed species (e.g. chickweed, lambsquarters, and nightshades.) Rotate beet, chard, and spinach to new fields [beds] in the spring and during the growing season. Avoid placing spring plantings near tunnels where winter greens were grown. Row covers or insect netting can be used to exclude flies if placed over the crop immediately after planting or before flies are active, but be sure not to cover crops in fields where susceptible crops were grown previously and where adult flies may be emerging, as they will get trapped under the cover.

Chemical controls must be used with caution on edible plants and must be applied at the right time. There are numerous species of leaf miner and some produce multiple generations in a season. Insecticidal soap is often recommended, however, my personal feeling is that its effect is limited because it must be sprayed directly on the pests which are usually inside the leaf. 

Some products containing Spinosad are approved for organic gardening. As with all products, it must be used exactly as directed, for the crops indicated, and in compliance with all warnings. 

Affecting leaves can be eaten if the damaged parts are trimmed. I my personal experience, I have found floating row cover to be the most effective solution if it is used from planting to harvest, assuming the miners are not already in the soil. 

I hope this information is helpful. Please write again whenever you have a gardening question.