Toilets, Sinks, Showers, Tubs and Disposals - kitchen sink backup

My kitchen sink fills up/backs up with water from time to time. I've notice that at times it does this when the dishwasher is running/draining. Also sometimes the dishwasher will not drain completely and will have standing water in the bottom of it. It seems a little too coincidential with the dishwasher and sink. I've taken appart what I could under the sink and have found no clogs. I've also used draino. Sometimes too, when just running water the sink will fill up until I turn on the disposal. I cannot feel anything in the disposal that would be clogging it up. I can live with the problem but if anyone has some advice I'd welcome it. Thanks.

OK, have you tried plunging the sink. To do this you will need to hold a stopper in one of the sinks, if a 2 bowl sink, while plunging the other.

It sound as if you have a partially plugged line.
Have you disconnected the trap and checked inside the trap for debris? Very common problem. Do you always run water while using the disposal? You should.
Whenever the sink backs up you will get water backing up into the dishwasher, unless yous system has an air gap.