Kitchen range hood

We are dissatisfied with the effectiveness of our downdraft vent for our island cooktop and want to install an overhead island vent. There is a second floor above the kitchen and therefore we want to vent it up between the ceiling and the second floor, make a turn, and out the side wall. Is this possbile? Is this safe?

The way you described your solution seems to be both possible and safe.  We have vented several over the range hood through the joists space of the kitchen ceiling to the exterior.  Depending on the size of the hood, typically given in CFM, this will determine the size of duct work required and the maximum length of the duct run to operate efficiently.  This information should be provided by the hood manufacturer.  Be aware, that each 90 degree turn can equal up to 25'.