I don't think this system really exists, but the Republic of China constitution (prior to the 2005 constitutional amendments) has a somewhat similar design. The ROC constitution establishes three (directly or indirectly) elected assemblies: the National Assembly, the Legislative Yuan (立法院), and the Control Yuan (監察院).
According to the 1946 ROC constitution, the National Assembly and the Legislative Yuan are directly elected by all citizens, while the Control Yuan is indirectly elected by provincial legislatures. The powers of the three assemblies are divided as following:
- Electing the President and Vice President
- Amending the constitution
- Initiative and referendum (創制復決), which are reserved powers that are not "activated" until some time in the future (explained below).
- Pass and repeal laws, budgets, treaties, declarations of war, etc.
- Vote of confidence on the Executive Yuan (i.e., cabinet)
- Advice and consent to presidential appointments
- Instigating & trying impeachments (subject to final approval by the National Assembly)
- Checking and supervising the executive
The Legislative Yuan is similar to parliaments in many parliamentary states, the National Assembly essentially holds the fundamental powers and sovereignty of the state (somewhat similar to the UK Parliament), while the Control Yuan is much like the US Senate stripped of its legislative powers.
The power of "initiative and referendum" is most similar to your "third chamber". Sun Yat-sen, who proposed the framework of the ROC constitution, believed that the people shall be able to directly interfere in legislation - by submitting them to popular referendum (and also by popular legislative initiative). However, China is very big, and he thus believed that popular referendum of laws is only appropriate at the local level. At the national level, this power shall be held by the members of the National Assembly, who acted as full-power representatives of the people.
However, at that time, there was a lot contention over this power, so the 1946 ROC constitution included a clause which said "the National Assembly shall have the powers of initiative and referendum after the people in more than half of all localities in the country have exercised these rights". However, this have not happened, while in 2005 the National Assembly was effective abolished, and the idea of "initiative and referendum" was also gone.