Lemon balm grows nicely in shade and makes a delicious pesto or refreshing accent to beverages.
Parsley fares pretty well inside, too, but needs warmer temperatures in order to thrive.
Basil actually doesn't do very well in mostly shade; it grows best in full sun.
For vegetables, it seems that leafy greens are easy to grow in shade (which helps prevent bolting, too), but I haven't tried growing greens indoors so I can't speak from experience on that one. Mother Earth News actually has a great chart with the minimum hours of sunlight per day that shade-friendly vegetables require; bok choi looks like it's the most shade-tolerant, requiring only 2 hours of sunlight per day.
As far as I know, most fruit requires full sun, but maybe someone else has experience successfully growing fruit inside with only partial sun.