I've never had to fix one but I know those types of faucets have a little diverter down in there that'll get stuck or your sprayer is getting plugged causing the diverter to not seal off the faucet side completely.
At the end of the hose between the water pipes is the spring loaded diverter valve. Inside i bet you will find a piece of scale or other stuff keeping it from closeing all the way when sprayer is in use. Just flush it out being careful of the spring. Good luck!