Water from sink draining into dishwasher, no air gap
having just redone the dishwasher, sink, disposal and faucet/drains in my kitchen I can hopefully help you here.  You shouldn't need an airgap for one.  I actually removed mine when I redid them because I found it to be ugly and both the dishwasher and disposal manuals say one was not necessary.  What you can do is loop the dishwasher drain hose so it reaches above the connection to the disposal, this should keep stuff from running backwards into the dishwasher.  I am however concerned that this is happening in the first place and might suggest checking your disposal to see if it is clogged or having other drainage issues as the water level in the disposal shouldn't ever get high enough for water to backwash down the to the dishwasher.  

Also running the dishwasher into the disposal is beneficial so any large food waste goes through the disposal instead of directly down your drain so I wouldn't change that part out.

I would also double check your manual for your dishwasher to see if it has special instructions for the connection without the airgap.