The washer has been overflowing during the drain cycles. I have been told by several plumbers that this line also handles the kitchen sink and dishwasher. Rarely if ever do I have the washer and dishwasher on at the same time. The kitchen sink by itself does not backup. However, when the washer drains water does come up in the bottom of the sink on both sides (disposal and sink) which are connected together under the sink into the one drain line for these items. I have had the line cleaned and checked for blockage all the way to the city connection. I have had the city clean out their pipe as well. Still the problem persists. I have gone online and realize that the vent pipe serving this line could be clogged or blocked causing the backup in the line. When the washer starts to drain all is well for a bit but I can hear the line filling and I stop the drainage. I hear the water flush out of the pipe and I start the washer again. I have to do this two and sometimes three times it drains depending on the size of the load in the washer. Given that the plumbers all say the line does not seem to be blocked by anything should I get someone on the roof the clean the vent pipe?

Snake both the kitchen and the washer vents. If that doesn't solve the problem then it sure sounds like you have a partial blockage downstream from the washer .

When the washer starts to drain all is well for a bit but I can hear the line filling This tells me that you have a partial blockage quite a way down the line. Perhaps the plumbers didn't put out enough snake. I'd snake that line again. Good luck, Tom