Does the word “episode” apply to each individual broadcast of a TV program, no matter what the content each time?
Solution 1:
An episode is something that has a beginning and an end:
An episode is a coherent narrative unit within a larger dramatic work.
When an episode is too long to be aired in a single continuous broadcast, we are talking about a multi-part episode:
A multi-part episode is used when a given plot development is, quite simply, too big for one time slot.
See examples of usage here and here..
Note: your use of the term broadcast is potentially misleading. The same episode - or a part - can be broadcast (aired) many times.