Business Structure

Your understanding is not really correct:
1) If both companies are owned by the same person, or one company owns the other, and they operate closely together, it may be possible for someone suing one to "pierce the corporate veil" (the same term, "corporate veil," is used whether the businesses are corporations or LLCs) and piece the protection of the first to get at the asserts of the second, too, on the grounds that the first LLC was not a legitimate LLC or did not have an independent existence and was, in essence, just a sham or artifice to defraud creditors, including "judgment creditors"--people who sue you and win. If a business is deliberately undercapitalized (left with insufficient money or other assets to pay common or reasonable liabilities) it is much more likely that its corporate veil can be pierced, so having an op co without assets is practically an invitation to have someone try to pierce the corporate veil and go after the other company.
2) If there is liability arising out of the assets owned by holding company, then the holding company would be liable anyway, notwithstanding the existence or presence of the operating company, since it provided or owned the thing causing the injury, harm, or cause of action.
In short, your scheme doesn't really provide any appreciable amount of protection beyond the protection for your personal asserts provided by having a single LLC. It does increase your cdosrts and complexities without gaining you much. Create a single LLC; regularly draw distributions of profits from it, so you don't leave more money sitting it than it reasonably needs for operations; and have good business liability insurance. That's how you protect yourself and your business.