That happened in '02, no?
You're actually thinking of 2000 here, and even then the timeline is pretty complicated.
Obviously the 2000 election is mostly remembered for the presidential result but the Senate results and the following developments were also quite interesting. Going into the election Republicans had a 54-46 majority, but the map had more upside for Democrats because it was the first election for this Senate class since the 1994 Republican Revolution. Indeed, it would be the first of three consecutive elections for this Senate class where Democrats would make a net gain (which is why there's so little room to play offense when it comes up again next year).
The Democrats picked up four seats, making the Senate 50-50. This allowed the Democrats to technically capture the Senate for the brief period between the beginning of the new Congress and the presidential inauguration on then-Vice President Al Gore's tie-breaking vote. Of course this only lasted a few weeks before Bush was sworn in, Dick Cheney now held the tie-breaking vote, and control of the Senate reverted to Republicans. But not for long, because in June Senator Jim Jeffords (R-VT) switched his affiliation to Independent and began to caucus with the Democrats, giving them an effective 51-49 majority. This arrangement would last until the 2002 midterms when, bucking the usual midterm pattern, Republicans made a net gain of two seats, giving them the majority again.
The story in the House for the 2000 cycle was far less interesting. Some seats got swapped around but the end result was a net gain of a single seat for the Democrats which allowed Republicans to retain control of the chamber by a slim margin.
EDIT: That's what I get for taking forever to compose my reply.
