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In a saucepan combine the broth and half of the milk. Heat over medium heat on the stove-top, for about 5 minutes or until steaming. Cover and keep hot.
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In a large, deep pot, heat oil over medium heat. Add onion, celery, garlic, dried herbs, salt and pepper, and sauté for about 5 minutes or until onions are softened. Add barley and flour; stir to coat well.
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Stir in hot broth mixture. Cover, reduce heat to low and simmer, stirring occasionally, for 25 minutes or until barley is almost tender. Add a little more of the milk if necessary to keep barley moist
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Meanwhile, heat remaining milk until steaming.
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Stir kidney or Romano beans, green beans and remaining hot milk into barley. Cover and simmer, stirring often, for 10 to 15 minutes or until barley is tender and green beans are tender-crisp. Adjust the heat as necessary to keep the pot at a steady simmer without boiling.
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Remove from heat and let stand for 5 to 10 minutes to thicken slightly. Drizzle in vinegar, stirring to combine.
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Serve sprinkled with parmesan if you choose