In March 1992 Burundi adopted a new constitution. It was promulgated on 13 March of that year, following a referendum four days earlier in which over 90% of those voting approved the new text.

Art. 61 stated that the president is directly elected for a five-year once-renewable term.

Art. 72 of the 1992 text stated that the president named the prime minister and ended his functions (i.e. a direct copy of the current French constitution. In fact, much of the constitution was a direct copy of the French one). However, in 1994 an amendment said that the president named the prime minister in conformity with the consensus framework that had just been adopted.

Art. 86 stated that the prime minister was part of the government.

Art. 89 said that the prime minister was responsible before the president and the National Assembly. So, Burundi was an example of a president-parliamentary form of semi-presidentialism.

Art. 134 stated that the government could ask for a vote of confidence in the Assembly. If defeated, by an absolute majority of votes, the government had to resign.

Art. 139 stated that the National Assembly could lodge a motion of censure. Again, if passed, with a three-fifths majority this time, the government had to resign.

As far as I understand it, the 1992 constitution was only officially suspended following the coup in July 1996. However, there was an earlier coup in October 1993 when the Tutsi-led army killed the Hutu president, Melchior Ndadaye, who had been elected in a pretty free and fair election just a few months earlier. There was then an agreement between the two sides in September 1994 (from where the aforementioned amendments to the constitution emanated). However, there was little stability, even though the two forces were nominally sharing powers.

There is a very informative article on the 1993 elections by Filip Reyntjens in The Journal of Modern African Studies, Vol. 31, No. 4. (Dec., 1993), pp. 563-583.

Previous posts on historic cases of semi-presidentialism:

Cuba

South Vietnam

Zaire

Central African Republic