When the main begins to get clogged up, liquids obviously take longer to pass the obstruction. By utilizing the garbage disposer, it is forcing the fluids into the pipe at a faster rate, so when you shut the disposal off, the fluids begin to back up. The same applies to a dishwasher. they use pumps to force the fluids into your main, but your faucet only works on gravity.
My advice is to contact a plumber, and ask him to snake your main line. If you do this during business hours mid week, the prices are pretty cheap...~$35.00 in my area. If you wait much longer, the stoppage will get worse and eventually completely stop up, and in my case, on a holiday, with a house full of family members, and late at night. That time it cost me about $250.00 to get the plumber out of bed!
Another solution it to rent the snake and do it yourself, but if you don't know what you are doing, you could cause serious damage to your drain lines.