if you want the two tasks to run *completely* independent of each other, your options are rather limited. Inquisit currently does not offer multiple, independent control structures that would allow running trials / blocks of trials in parallel. Instead, Inquisit is restricted to running a single trial at a given time as well as collecting a single response per trial. Inquisit is also restricted to a single response modality per trial (i.e. it will only accept keyboard OR mouse OR response box, etc. input in a given trial). However, there might be two workaround strategies:
(1) You could sync *two* computers running Inquisit 3 via TTL signals. Each computer would then run one of the tasks. However, I don't think this would be a viable strategy for the specific tasks you're aiming to combine.
(2) If you have a skilled flash programmer at hand, one of the tasks could be implemented via flash. As Inquisit is able to handle interactive flash objects as 'background stimuli' during a block of its own trials, this could be a valid implementation strategy.
But, in sum, Inquisit currently isn't really designed to handle dual task paradigms.
Best wishes from a fellow Inquisit user,
P.S.: The dual task issue has been discussed here a few times, so you might also want to do a forum search for additional information.