Place split peas, lima beans, barley and stock in a large pot, bring to a boil, reduce heat and add bay leaves and celery seed. Cover and cook over low heat for 1 hour.
Add remaining ingredients and cook for 1 additional hour.
If you want to make this without the lima beans, increase the split peas to 2 cups and reduce the initial cooking time to ½ hour. This recipe freezes and reheats well. For a delicious smoky flavor, try adding a couple drops of liquid smoke to the soup about 15 minutes before the end of the cooking time.