It is the rare (and fortunate) undergraduate who has so many interview invitations that it causes problems with their coursework.
When you get your first interview invitation, speak to your professors, tell them about your interview, and ask to reschedule anything that conflicts. If you ask to be notified of any assignments early enough to complete it and turn it in early (vs. late) it'll be hard for them to refuse. (This is where having good relationships with your professors comes in handy.)
As has been suggested, to the extent you can, schedule your classes for fewer days -- though if your interviews are on those dates, you're still SOL. And take your most important/difficult classes during other semesters. If you can, also arrange it so you can drop a class, if worse comes to worst.