'On the schedule' seems normal because schedules are normally 'on' something; paper, a board, a webpage - where people can read it. 'In the schedule' doesn't seem to make sense in that way..

It's on the schedule in the same way a writing or drawing would be on the board or on a picture. "In" means that it would be inside the schedule not on the surface of the paper.

On the schedule :)

Hi Katya, I would like to add that we use "on" for information that is transmitted through a medium. This is the case for your sentence: there is a schedule (be it printed on paper, shown on a screen or otherwise) which contains information about deadlines, time of arrival, time of departure and so on. Another example: A picture of the fugitive was shown ON television last night. / The games will be aired live ON CNN tonight.

"What's on the schedule today?" On the schedule is correct. Also, you can say, "Is the plane on schedule?"