Recent observations of CLUSTER have reconfirmed the recurring presence of bifurcated current sheets. The present paper revisits the model of Schindler and Birn (2002) to describe analytically bifurcated current sheets. Our contributions are in order. First, we describe a number of analytical velocity distribution functions that lead to bifurcated current sheets. Second, we derive necessary and sufficient conditions that determine when current sheets can be produced within the mathematical model of Schindler and Birn (2002). Third, we present a class of bifurcated current sheets, and we describe their properties. Fourth, we study the stability of bifurcated current sheets to the tearing instability finding that bifurcated current sheets tend to be more stable. Finally, we investigate the stability of bifurcated current sheets to the lower hybrid drift instability (LHDI) and kinking instability proving their presence. The work reported here is intended to extend and investigate the properties of instabilities from the typical but academic case of the Harris current sheet to current sheet equilibria that are more realisticly representative of the real magnetotail.