Herb garden infested. Looking for a non chemical remedy. Help!

Infested with what? Makes a difference as to type of remedy. More info please!

diluted distilled white or apple cider vinegar does a number on weeds. You say infested, infested with what?

Use a Horticultral soap and apply repeatedly

Try diotomateus earth (DE) powder or a product called Captain Jack's natural pesticide or mix 1 part peroxide to 15 parts water & spray them. All are safe ! Hope this helps!

I like to plant peppermint near everything. I also mix up hot pepper flakes and hot pepper juice and spray. I have also used white vinegar and a few drops of peppermint oil - the kind you could safely ingest.

Shredded irish spring soap,sprinkled in and around garden keeps a host of critters away!