I would think if you are still employed in some capacity, you do not qualify for unemployment insurance, as it is for subsistence living while unemployed - and you are still employed (just not FULLY employed).
However, who knows about the vagueries of the law . . . so it would be in your best interests to make a trip to an ESC office (I know - not the most fun thing to do - especially if you wait for hours just to find out you qualify for nothing). However, what if you WOULD qualify, and then they treat your other income as part time work and deduct it - leaving you with some money each week. It would be worth finding out b/c even $150 a week could make a huge difference in the long run.
So I would advise going to an ESC office, explaining the situation and finding out firsthand.