1996 jeep cherokee sport headlight low beams wont work. high beams and everything else work, but no low beams.

Try taking your tilt steering(steeringwheel) and check which setting its on if the tilt steering is all the way down click it up to the next setting and then try your low beams if that still doesn't work try it one more click up you might have a short or pinched wire in your wheel colum

The low beam side of the light in blown

These jeeps have a daytime running light module (canada), that the low beam circuit runs through it, if defective, no low beams, also the multifunction switch is part of this circuit to, are the fuses good ? you can back probe the mfs, with a volt meter, remove the steering column covers, the mfs is part of the turn signal switch, schematics are avaible online from Napa, Part Source, MItchel on demand. GOOD LUCK. RDJRP